We have the following **284 statistics** on **Permutations** in the database:

St000001
Permutations ⟶ ℤ

The number of ways to write a permutation as a minimal length product of simple t....

St000002
Permutations ⟶ ℤ

The number of occurrences of the pattern 123 in a permutation.

St000004
Permutations ⟶ ℤ

The major index of a permutation.

St000007
Permutations ⟶ ℤ

The number of saliances of the permutation.

St000018
Permutations ⟶ ℤ

The number of inversions of a permutation.

St000019
Permutations ⟶ ℤ

The cardinality of the complement of the connectivity set.

St000020
Permutations ⟶ ℤ

The rank of the permutation.

St000021
Permutations ⟶ ℤ

The number of descents of a permutation.

St000022
Permutations ⟶ ℤ

The number of fixed points of a permutation.

St000023
Permutations ⟶ ℤ

The number of inner peaks of a permutation.

St000028
Permutations ⟶ ℤ

The number of stack-sorts needed to sort a permutation.

St000029
Permutations ⟶ ℤ

The depth of a permutation.

St000030
Permutations ⟶ ℤ

The sum of the descent differences of a permutations.

St000031
Permutations ⟶ ℤ

The number of cycles in the cycle decomposition of a permutation.

St000033
Permutations ⟶ ℤ

The number of permutations greater than or equal to the given permutation in (str....

St000034
Permutations ⟶ ℤ

The maximum defect over any reduced expression for a permutation and any subexpre....

St000035
Permutations ⟶ ℤ

The number of left outer peaks of a permutation.

St000036
Permutations ⟶ ℤ

The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by th....

St000037
Permutations ⟶ ℤ

The sign of a permutation.

St000039
Permutations ⟶ ℤ

The number of crossings of a permutation.

St000040
Permutations ⟶ ℤ

The number of regions of inversion arrangement of a permutation.

St000054
Permutations ⟶ ℤ

The first entry of the permutation.

St000055
Permutations ⟶ ℤ

The inversion sum of a permutation.

St000056
Permutations ⟶ ℤ

The decomposition (or block) number of a permutation.

St000058
Permutations ⟶ ℤ

The order of a permutation.

St000060
Permutations ⟶ ℤ

The greater neighbor of the maximum.

St000062
Permutations ⟶ ℤ

The length of the longest increasing subsequence of the permutation.

St000064
Permutations ⟶ ℤ

The number of one-box pattern of a permutation.

St000078
Permutations ⟶ ℤ

The number of alternating sign matrices whose left key is the permutation.

St000092
Permutations ⟶ ℤ

The number of outer peaks of a permutation.

St000099
Permutations ⟶ ℤ

The number of valleys of a permutation, including the boundary.

St000109
Permutations ⟶ ℤ

The number of elements less than or equal to the given element in Bruhat order.

St000110
Permutations ⟶ ℤ

The number of permutations less than or equal to given permutation in left weak o....

St000111
Permutations ⟶ ℤ

The sum of the descent tops (or Genocchi descents) of a permutation.

St000119
Permutations ⟶ ℤ

The number of occurrences of the pattern 321 in a permutation.

St000123
Permutations ⟶ ℤ

The difference in Coxeter length of a permutation and its image under the Simion-....

St000124
Permutations ⟶ ℤ

The cardinality of the preimage of the Simion-Schmidt map.

St000133
Permutations ⟶ ℤ

The "bounce" of a permutation.

St000141
Permutations ⟶ ℤ

The maximum drop size of a permutation.

St000153
Permutations ⟶ ℤ

The number of adjacent cycles of a permutation.

St000154
Permutations ⟶ ℤ

The sum of the descent bottoms of a permutation.

St000155
Permutations ⟶ ℤ

The number of exceedances (also excedences) of a permutation.

St000156
Permutations ⟶ ℤ

The Denert index of a permutation.

St000162
Permutations ⟶ ℤ

The number of nontrivial cycles of a permutation $\pi$ in its cycle decomposition.

St000209
Permutations ⟶ ℤ

Maximum difference of elements in cycles.

St000210
Permutations ⟶ ℤ

Minimum over maximum difference of elements in cycles.

St000213
Permutations ⟶ ℤ

The number of weak exceedances (also weak excedences) of a permutation.

St000214
Permutations ⟶ ℤ

The number of adjacencies (or small descents) of a permutation.

St000215
Permutations ⟶ ℤ

The number of adjacencies of a permutation, 0 appended.

St000216
Permutations ⟶ ℤ

The absolute length of a permutation.

St000217
Permutations ⟶ ℤ

The number of occurrences of the pattern 312 in a permutation.

St000218
Permutations ⟶ ℤ

The number of occurrences of the pattern 213 in a permutation.

St000219
Permutations ⟶ ℤ

The number of occurrences of the pattern 231 in a permutation.

St000220
Permutations ⟶ ℤ

The number of occurrences of the pattern 132 in a permutation.

St000221
Permutations ⟶ ℤ

The number of strong fixed points of a permutation.

St000222
Permutations ⟶ ℤ

The number of alignments in the permutation.

St000223
Permutations ⟶ ℤ

The number of nestings in the permutation.

St000224
Permutations ⟶ ℤ

The sorting index of a permutation.

St000226
Permutations ⟶ ℤ

The convexity of a permutation.

St000234
Permutations ⟶ ℤ

The number of global ascents of a permutation.

St000235
Permutations ⟶ ℤ

The number of indices $i$ such that $\pi_i \neq i+1$ considered cyclically.

St000236
Permutations ⟶ ℤ

The number of indices $i$ such that $\pi_i \in \{ i,i+1 \}$ considered cyclically.

St000237
Permutations ⟶ ℤ

The number of indices $i$ such that $\pi_i=i+1$.

St000238
Permutations ⟶ ℤ

The number of indices $i$ such that $\pi_i \notin \{i,i+1\}$.

St000239
Permutations ⟶ ℤ

The number of indices $i$ such that $\pi_i \in \{i,i+1\}$.

St000240
Permutations ⟶ ℤ

The number of indices $i$ for which $\pi_i \neq i+1$.

St000241
Permutations ⟶ ℤ

The number of indices $i$ such that $\pi_i = i+1$ considered cyclically.

St000242
Permutations ⟶ ℤ

The number of indices $i$ such that $\pi_i \notin \{ i,i+1 \}$ considered cyclically.....

St000243
Permutations ⟶ ℤ

The number of cyclic valleys and cyclic peaks of a permutation.

St000245
Permutations ⟶ ℤ

The number of ascents of a permutation.

St000246
Permutations ⟶ ℤ

The number of non-inversions of a permutation.

St000255
Permutations ⟶ ℤ

The number of reduced Kogan faces with the permutation as type.

St000279
Permutations ⟶ ℤ

The size of the preimage of the map 'cycle-as-one-line notation' from Permutation....

St000280
Permutations ⟶ ℤ

The size of the preimage of the map 'to labelling permutation' from Parking funct....

St000304
Permutations ⟶ ℤ

The load of a permutation.

St000305
Permutations ⟶ ℤ

The inverse major index of a permutation.

St000308
Permutations ⟶ ℤ

The height of the tree associated to a permutation.

St000314
Permutations ⟶ ℤ

The number of left-to-right-maxima of a permutation.

St000316
Permutations ⟶ ℤ

The number of non-left-to-right-maxima of a permutation.

St000317
Permutations ⟶ ℤ

The cycle descent number of a permutation.

St000324
Permutations ⟶ ℤ

The shape of the tree associated to a permutation.

St000325
Permutations ⟶ ℤ

The width of the tree associated to a permutation.

St000333
Permutations ⟶ ℤ

The dez statistic, the number of descents of a permutation after replacing fixed ....

St000334
Permutations ⟶ ℤ

The maz index, the major index of a permutation after replacing fixed points by z....

St000337
Permutations ⟶ ℤ

The lec statistic, the sum of the inversion numbers of the hook factors of a perm....

St000338
Permutations ⟶ ℤ

The number of pixed points of a permutation.

St000339
Permutations ⟶ ℤ

The maf index of a permutation.

St000341
Permutations ⟶ ℤ

The non-inversion sum of a permutation.

St000342
Permutations ⟶ ℤ

The cosine of a permutation.

St000352
Permutations ⟶ ℤ

The Elizalde-Pak rank of a permutation.

St000353
Permutations ⟶ ℤ

The number of inner valleys of a permutation.

St000354
Permutations ⟶ ℤ

The number of recoils of a permutation.

St000355
Permutations ⟶ ℤ

The number of occurrences of the pattern 21-3.

St000356
Permutations ⟶ ℤ

The number of occurrences of the pattern 13-2.

St000357
Permutations ⟶ ℤ

The number of occurrences of the pattern 12-3.

St000358
Permutations ⟶ ℤ

The number of occurrences of the pattern 31-2.

St000359
Permutations ⟶ ℤ

The number of occurrences of the pattern 23-1.

St000360
Permutations ⟶ ℤ

The number of occurrences of the pattern 32-1.

St000365
Permutations ⟶ ℤ

The number of double ascents of a permutation.

St000366
Permutations ⟶ ℤ

The number of double descents of a permutation.

St000367
Permutations ⟶ ℤ

The number of simsun double descents of a permutation.

St000371
Permutations ⟶ ℤ

The number of mid points of decreasing subsequences of length 3 in a permutation.....

St000372
Permutations ⟶ ℤ

The number of mid points of increasing subsequences of length 3 in a permutation.....

St000373
Permutations ⟶ ℤ

The number of weak exceedences of a permutation that are also mid-points of a dec....

St000374
Permutations ⟶ ℤ

The number of exclusive right-to-left minima of a permutation.

St000375
Permutations ⟶ ℤ

The number of non weak exceedences of a permutation that are mid-points of a decr....

St000401
Permutations ⟶ ℤ

The size of the symmetry class of a permutation.

St000402
Permutations ⟶ ℤ

Half the size of the symmetry class of a permutation.

St000404
Permutations ⟶ ℤ

The number of occurrences of the pattern 3241 or of the pattern 4231 in a permuta....

St000405
Permutations ⟶ ℤ

The number of occurrences of the pattern 1324 in a permutation.

St000406
Permutations ⟶ ℤ

The number of occurrences of the pattern 3241 in a permutation.

St000407
Permutations ⟶ ℤ

The number of occurrences of the pattern 2143 in a permutation.

St000408
Permutations ⟶ ℤ

The number of occurrences of the pattern 4231 in a permutation.

St000423
Permutations ⟶ ℤ

The number of occurrences of the pattern 123 or of the pattern 132 in a permutati....

St000424
Permutations ⟶ ℤ

The number of occurrences of the pattern 132 or of the pattern 231 in a permutati....

St000425
Permutations ⟶ ℤ

The number of occurrences of the pattern 132 or of the pattern 213 in a permutati....

St000426
Permutations ⟶ ℤ

The number of occurrences of the pattern 132 or of the pattern 312 in a permutati....

St000427
Permutations ⟶ ℤ

The number of occurrences of the pattern 123 or of the pattern 231 in a permutati....

St000428
Permutations ⟶ ℤ

The number of occurrences of the pattern 123 or of the pattern 213 in a permutati....

St000429
Permutations ⟶ ℤ

The number of occurrences of the pattern 123 or of the pattern 321 in a permutati....

St000430
Permutations ⟶ ℤ

The number of occurrences of the pattern 123 or of the pattern 312 in a permutati....

St000431
Permutations ⟶ ℤ

The number of occurrences of the pattern 213 or of the pattern 321 in a permutati....

St000432
Permutations ⟶ ℤ

The number of occurrences of the pattern 231 or of the pattern 312 in a permutati....

St000433
Permutations ⟶ ℤ

The number of occurrences of the pattern 132 or of the pattern 321 in a permutati....

St000434
Permutations ⟶ ℤ

The number of occurrences of the pattern 213 or of the pattern 312 in a permutati....

St000435
Permutations ⟶ ℤ

The number of occurrences of the pattern 213 or of the pattern 231 in a permutati....

St000436
Permutations ⟶ ℤ

The number of occurrences of the pattern 231 or of the pattern 321 in a permutati....

St000437
Permutations ⟶ ℤ

The number of occurrences of the pattern 312 or of the pattern 321 in a permutati....

St000440
Permutations ⟶ ℤ

The number of occurrences of the pattern 4132 or of the pattern 4231 in a permuta....

St000441
Permutations ⟶ ℤ

The number of successions (or small ascents) of a permutation.

St000446
Permutations ⟶ ℤ

The disorder of a permutation.

St000451
Permutations ⟶ ℤ

The length of the longest pattern of the form k 1 2.

St000457
Permutations ⟶ ℤ

The number of occurrences of one of the patterns 132, 213 or 321 in a permutation....

St000458
Permutations ⟶ ℤ

The number of permutations obtained by switching adjacencies or successions.

St000461
Permutations ⟶ ℤ

The rix statistic of a permutation.

St000462
Permutations ⟶ ℤ

The major index minus the number of excedences of a permutation.

St000463
Permutations ⟶ ℤ

The number of admissible inversions of a permutation.

St000470
Permutations ⟶ ℤ

The number of runs in a permutation.

St000471
Permutations ⟶ ℤ

The sum of the ascent tops of a permutation.

St000472
Permutations ⟶ ℤ

The sum of the ascent bottoms of a permutation.

St000483
Permutations ⟶ ℤ

The number of times a permutation switches from increasing to decreasing or decre....

St000484
Permutations ⟶ ℤ

The sum of St000483 over all subsequences of length at least three.

St000485
Permutations ⟶ ℤ

The length of the longest cycle of a permutation.

St000486
Permutations ⟶ ℤ

The number of cycles of length at least 3 of a permutation.

St000487
Permutations ⟶ ℤ

The length of the shortest cycle of a permutation.

St000488
Permutations ⟶ ℤ

The number of cycles of a permutation of length at most 2.

St000489
Permutations ⟶ ℤ

The number of cycles of a permutation of length at most 3.

St000494
Permutations ⟶ ℤ

The number of inversions of distance at most 3 of a permutation.

St000495
Permutations ⟶ ℤ

The number of inversions of distance at most 2 of a permutation.

St000500
Permutations ⟶ ℤ

Eigenvalues of the random-to-random operator acting on the regular representation....

St000501
Permutations ⟶ ℤ

The size of the first part in the decomposition of a permutation.

St000516
Permutations ⟶ ℤ

The number of stretching pairs of a permutation.

St000520
Permutations ⟶ ℤ

The number of patterns in a permutation.

St000530
Permutations ⟶ ℤ

The number of permutations with the same descent word as the given permutation.

St000534
Permutations ⟶ ℤ

The number of 2-rises of a permutation.

St000538
Permutations ⟶ ℤ

The number of even inversions of a permutation.

St000539
Permutations ⟶ ℤ

The number of odd inversions of a permutation.

St000541
Permutations ⟶ ℤ

The number of indices greater than or equal to 2 of a permutation such that all s....

St000542
Permutations ⟶ ℤ

The number of left-to-right-minima of a permutation.

St000545
Permutations ⟶ ℤ

The number of parabolic double cosets with minimal element being the given permut....

St000546
Permutations ⟶ ℤ

The number of global descents of a permutation.

St000570
Permutations ⟶ ℤ

The Edelman-Greene number of a permutation.

St000616
Permutations ⟶ ℤ

The inversion index of a permutation.

St000619
Permutations ⟶ ℤ

The number of cyclic descents of a permutation.

St000622
Permutations ⟶ ℤ

The number of occurrences of the patterns 2143 or 4231 in a permutation.

St000623
Permutations ⟶ ℤ

The number of occurrences of the pattern 52341 in a permutation.

St000624
Permutations ⟶ ℤ

The normalized sum of the minimal distances to a greater element.

St000625
Permutations ⟶ ℤ

The sum of the minimal distances to a greater element.

St000638
Permutations ⟶ ℤ

The number of up-down runs of a permutation.

St000646
Permutations ⟶ ℤ

The number of big ascents of a permutation.

St000647
Permutations ⟶ ℤ

The number of big descents of a permutation.

St000648
Permutations ⟶ ℤ

The number of 2-excedences of a permutation.

St000649
Permutations ⟶ ℤ

The number of 3-excedences of a permutation.

St000650
Permutations ⟶ ℤ

The number of 3-rises of a permutation.

St000651
Permutations ⟶ ℤ

The maximal size of a rise in a permutation.

St000652
Permutations ⟶ ℤ

The maximal difference between successive positions of a permutation.

St000653
Permutations ⟶ ℤ

The last descent of a permutation.

St000654
Permutations ⟶ ℤ

The first descent of a permutation.

St000662
Permutations ⟶ ℤ

The staircase size of the code of a permutation.

St000663
Permutations ⟶ ℤ

The number of right floats of a permutation.

St000664
Permutations ⟶ ℤ

The number of right ropes of a permutation.

St000665
Permutations ⟶ ℤ

The number of rafts of a permutation.

St000666
Permutations ⟶ ℤ

The number of right tethers of a permutation.

St000669
Permutations ⟶ ℤ

The number of permutations obtained by switching ascents or descents of size 2.

St000670
Permutations ⟶ ℤ

The reversal length of a permutation.

St000672
Permutations ⟶ ℤ

The number of minimal elements in Bruhat order not less than the permutation.

St000673
Permutations ⟶ ℤ

The size of the support of a permutation.

St000677
Permutations ⟶ ℤ

The standardized bi-alternating inversion number of a permutation.

St000690
Permutations ⟶ ℤ

The size of the conjugacy class of a permutation.

St000692
Permutations ⟶ ℤ

Babson and Steingrímsson's statistic stat of a permutation.

St000694
Permutations ⟶ ℤ

The number of affine bounded permutations that project to a given permutation.

St000696
Permutations ⟶ ℤ

The number of cycles in the breakpoint graph of a permutation.

St000702
Permutations ⟶ ℤ

The number of weak deficiencies of a permutation.

St000703
Permutations ⟶ ℤ

The number of deficiencies of a permutation.

St000709
Permutations ⟶ ℤ

The number of occurrences of 14-2-3 or 14-3-2.

St000710
Permutations ⟶ ℤ

The number of big deficiencies of a permutation.

St000711
Permutations ⟶ ℤ

The number of big exceedences of a permutation.

St000724
Permutations ⟶ ℤ

The label of the leaf of the path following the smaller label in the increasing b....

St000725
Permutations ⟶ ℤ

The smallest label of a leaf of the increasing binary tree associated to a permut....

St000726
Permutations ⟶ ℤ

The normalized sum of the leaf labels of the increasing binary tree associated to....

St000727
Permutations ⟶ ℤ

The largest label of a leaf in the binary search tree associated with the permuta....

St000731
Permutations ⟶ ℤ

The number of double exceedences of a permutation.

St000732
Permutations ⟶ ℤ

The number of double deficiencies of a permutation.

St000740
Permutations ⟶ ℤ

The last entry of a permutation.

St000742
Permutations ⟶ ℤ

The number of big ascents of a permutation after adding the value $\pi(0) = 0$.

St000750
Permutations ⟶ ℤ

The number of occurrences of the pattern 4213 in a permutation.

St000751
Permutations ⟶ ℤ

The number of occurrences of either of the pattern 2143 or 2143 in a permutation.....

St000756
Permutations ⟶ ℤ

The sum of the positions of the left to right maxima of a permutation.

St000779
Permutations ⟶ ℤ

The tier of a permutation.

St000794
Permutations ⟶ ℤ

The mak of a permutation.

St000795
Permutations ⟶ ℤ

The mad of a permutation.

St000796
Permutations ⟶ ℤ

The stat' of a permutation.

St000797
Permutations ⟶ ℤ

The stat`` of a permutation.

St000798
Permutations ⟶ ℤ

The makl of a permutation.

St000799
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |213 in a permutation.

St000800
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |231 in a permutation.

St000801
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |312 in a permutation.

St000802
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |321 in a permutation.

St000803
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |132 in a permutation.

St000804
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |123 in a permutation.

St000809
Permutations ⟶ ℤ

The reduced reflection length of the permutation.

St000824
Permutations ⟶ ℤ

The sum of the number of descents and the number of recoils of a permutation.

St000825
Permutations ⟶ ℤ

The sum of the number of major and the inverse major index of a permutation.

St000828
Permutations ⟶ ℤ

The spearman's rho of a permutation and the identity permutation.

St000829
Permutations ⟶ ℤ

The Ulam distance of a permutation to the identity permutation.

St000830
Permutations ⟶ ℤ

The total displacement of a permutation.

St000831
Permutations ⟶ ℤ

The number of indices that are either descents or recoils.

St000832
Permutations ⟶ ℤ

The number of permutations obtained by reversing blocks of three consecutive numb....

St000833
Permutations ⟶ ℤ

The comajor index of a permutation.

St000834
Permutations ⟶ ℤ

The number of right outer peaks of a permutation.

St000836
Permutations ⟶ ℤ

The number of descents of distance 2 of a permutation.

St000837
Permutations ⟶ ℤ

The number of ascents of distance 2 of a permutation.

St000842
Permutations ⟶ ℤ

The breadth of a permutation.

St000844
Permutations ⟶ ℤ

The size of the largest block in the direct sum decomposition of a permutation.

St000862
Permutations ⟶ ℤ

The number of parts of the shifted shape of a permutation.

St000863
Permutations ⟶ ℤ

The length of the first row of the shifted shape of a permutation.

St000864
Permutations ⟶ ℤ

The number of circled entries of the shifted recording tableau of a permutation.

St000866
Permutations ⟶ ℤ

The number of admissible inversions of a permutation in the sense of Shareshian-W....

St000868
Permutations ⟶ ℤ

The aid statistic in the sense of Shareshian-Wachs.

St000871
Permutations ⟶ ℤ

The number of very big ascents of a permutation.

St000872
Permutations ⟶ ℤ

The number of very big descents of a permutation.

St000873
Permutations ⟶ ℤ

The aix statistic of a permutation.

St000879
Permutations ⟶ ℤ

The number of long braid edges in the graph of braid moves of a permutation.

St000880
Permutations ⟶ ℤ

The number of connected components of long braid edges in the graph of braid move....

St000881
Permutations ⟶ ℤ

The number of short braid edges in the graph of braid moves of a permutation.

St000882
Permutations ⟶ ℤ

The number of connected components of short braid edges in the graph of braid mov....

St000883
Permutations ⟶ ℤ

The number of longest increasing subsequences of a permutation.

St000884
Permutations ⟶ ℤ

The number of isolated descents of a permutation.

St000886
Permutations ⟶ ℤ

The number of permutations with the same antidiagonal sums.

St000887
Permutations ⟶ ℤ

The maximal number of nonzero entries on a diagonal of a permutation matrix.

St000891
Permutations ⟶ ℤ

The number of distinct diagonal sums of a permutation matrix.

St000923
Permutations ⟶ ℤ

The minimal number with no two order isomorphic substrings of this length in a pe....

St000956
Permutations ⟶ ℤ

The maximal displacement of a permutation.

St000957
Permutations ⟶ ℤ

The number of Bruhat lower covers of a permutation.

St000958
Permutations ⟶ ℤ

The number of Bruhat factorizations of a permutation.

St000959
Permutations ⟶ ℤ

The number of strong Bruhat factorizations of a permutation.

St000961
Permutations ⟶ ℤ

The shifted major index of a permutation.

St000962
Permutations ⟶ ℤ

The 3-shifted major index of a permutation.

St000963
Permutations ⟶ ℤ

The 2-shifted major index of a permutation.

St000988
Permutations ⟶ ℤ

The orbit size of a permutation under Foata's bijection.

St000989
Permutations ⟶ ℤ

The number of final rises of a permutation.

St000990
Permutations ⟶ ℤ

The first ascent of a permutation.

St000991
Permutations ⟶ ℤ

The number of right-to-left minima of a permutation.

St000994
Permutations ⟶ ℤ

The number of cycle peaks and the number of cycle valleys of a permutation.

St000996
Permutations ⟶ ℤ

The number of exclusive left-to-right maxima of a permutation.

St001004
Permutations ⟶ ℤ

The number of indices that are either left-to-right maxima or right-to-left minim....

St001005
Permutations ⟶ ℤ

The number of indices for a permutation that are either left-to-right maxima or r....

St001052
Permutations ⟶ ℤ

The length of the exterior of a permutation.

St001059
Permutations ⟶ ℤ

Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation.

St001061
Permutations ⟶ ℤ

The number of indices that are both descents and recoils of a permutation.

St001074
Permutations ⟶ ℤ

The number of inversions of the cyclic embedding of a permutation.

St001076
Permutations ⟶ ℤ

The minimal length of a factorization of a permutation into transpositions that a....

St001077
Permutations ⟶ ℤ

The minimal length of a factorization of a permutation into star transpositions.

St001078
Permutations ⟶ ℤ

The minimal number of occurrences of (12) in a factorization of a permutation int....

St001079
Permutations ⟶ ℤ

The minimal length of a factorization of a permutation using the permutations (12....

St001080
Permutations ⟶ ℤ

The minimal length of a factorization of a permutation using the transposition (1....

St001081
Permutations ⟶ ℤ

The number of minimal length factorizations of a permutation into star transposit....

St001082
Permutations ⟶ ℤ

The number of boxed occurrences of 123 in a permutation.

St001083
Permutations ⟶ ℤ

The number of boxed occurrences of 132 in a permutation.

St001084
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |1-23 in a permutation.

St001085
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |21-3 in a permutation.

St001086
Permutations ⟶ ℤ

The number of occurrences of the consecutive pattern 132 in a permutation.

St001087
Permutations ⟶ ℤ

The number of occurrences of the vincular pattern |12-3 in a permutation.

St001090
Permutations ⟶ ℤ

The number of pop-stack-sorts needed to sort a permutation.