***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000959 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of strong Bruhat factorizations of a permutation. This is, the number of factorizations $\pi = t_1 \cdots t_\ell$ for transpositions $\{ t_i \mid 1 \leq i \leq \ell\}$ such that $t_1 \cdots t_i$ has more inversions than $t_1 \cdots t_{i-1}$ for all $1 \leq i \leq \ell$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: @cached_function def Transpositions(n): return Permutations(n).conjugacy_class([2]+[1]*(n-2)) @cached_function def strong_Bruhat_factorizations(pi): inv = pi.number_of_inversions() if inv == 0: return 1 else: facs = 0 for t in Transpositions(len(pi)): tau = pi*t if tau.number_of_inversions() < inv: facs += strong_Bruhat_factorizations(tau) return facs def statistic(pi): return strong_Bruhat_factorizations(pi) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 5 [1,2,3,4] => 1 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 5 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 6 [2,4,1,3] => 6 [2,4,3,1] => 18 [3,1,2,4] => 2 [3,1,4,2] => 6 [3,2,1,4] => 5 [3,2,4,1] => 18 [3,4,1,2] => 22 [3,4,2,1] => 62 [4,1,2,3] => 6 [4,1,3,2] => 18 [4,2,1,3] => 18 [4,2,3,1] => 73 [4,3,1,2] => 62 [4,3,2,1] => 210 [1,2,3,4,5] => 1 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 2 [1,2,5,3,4] => 2 [1,2,5,4,3] => 5 [1,3,2,4,5] => 1 [1,3,2,5,4] => 2 [1,3,4,2,5] => 2 [1,3,4,5,2] => 6 [1,3,5,2,4] => 6 [1,3,5,4,2] => 18 [1,4,2,3,5] => 2 [1,4,2,5,3] => 6 [1,4,3,2,5] => 5 [1,4,3,5,2] => 18 [1,4,5,2,3] => 22 [1,4,5,3,2] => 62 [1,5,2,3,4] => 6 [1,5,2,4,3] => 18 [1,5,3,2,4] => 18 [1,5,3,4,2] => 73 [1,5,4,2,3] => 62 [1,5,4,3,2] => 210 [2,1,3,4,5] => 1 [2,1,3,5,4] => 2 [2,1,4,3,5] => 2 [2,1,4,5,3] => 6 [2,1,5,3,4] => 6 [2,1,5,4,3] => 18 [2,3,1,4,5] => 2 [2,3,1,5,4] => 6 [2,3,4,1,5] => 6 [2,3,4,5,1] => 24 [2,3,5,1,4] => 24 [2,3,5,4,1] => 86 [2,4,1,3,5] => 6 [2,4,1,5,3] => 24 [2,4,3,1,5] => 18 [2,4,3,5,1] => 86 [2,4,5,1,3] => 106 [2,4,5,3,1] => 352 [2,5,1,3,4] => 24 [2,5,1,4,3] => 86 [2,5,3,1,4] => 86 [2,5,3,4,1] => 418 [2,5,4,1,3] => 352 [2,5,4,3,1] => 1382 [3,1,2,4,5] => 2 [3,1,2,5,4] => 6 [3,1,4,2,5] => 6 [3,1,4,5,2] => 24 [3,1,5,2,4] => 24 [3,1,5,4,2] => 86 [3,2,1,4,5] => 5 [3,2,1,5,4] => 18 [3,2,4,1,5] => 18 [3,2,4,5,1] => 86 [3,2,5,1,4] => 86 [3,2,5,4,1] => 354 [3,4,1,2,5] => 22 [3,4,1,5,2] => 106 [3,4,2,1,5] => 62 [3,4,2,5,1] => 352 [3,4,5,1,2] => 508 [3,4,5,2,1] => 1634 [3,5,1,2,4] => 106 [3,5,1,4,2] => 462 [3,5,2,1,4] => 352 [3,5,2,4,1] => 1958 [3,5,4,1,2] => 1926 [3,5,4,2,1] => 7160 [4,1,2,3,5] => 6 [4,1,2,5,3] => 24 [4,1,3,2,5] => 18 [4,1,3,5,2] => 86 [4,1,5,2,3] => 106 [4,1,5,3,2] => 352 [4,2,1,3,5] => 18 [4,2,1,5,3] => 86 [4,2,3,1,5] => 73 [4,2,3,5,1] => 418 [4,2,5,1,3] => 462 [4,2,5,3,1] => 1958 [4,3,1,2,5] => 62 [4,3,1,5,2] => 352 [4,3,2,1,5] => 210 [4,3,2,5,1] => 1382 [4,3,5,1,2] => 1926 [4,3,5,2,1] => 7160 [4,5,1,2,3] => 508 [4,5,1,3,2] => 1926 [4,5,2,1,3] => 1926 [4,5,2,3,1] => 10544 [4,5,3,1,2] => 8022 [4,5,3,2,1] => 34266 [5,1,2,3,4] => 24 [5,1,2,4,3] => 86 [5,1,3,2,4] => 86 [5,1,3,4,2] => 418 [5,1,4,2,3] => 352 [5,1,4,3,2] => 1382 [5,2,1,3,4] => 86 [5,2,1,4,3] => 354 [5,2,3,1,4] => 418 [5,2,3,4,1] => 2381 [5,2,4,1,3] => 1958 [5,2,4,3,1] => 9234 [5,3,1,2,4] => 352 [5,3,1,4,2] => 1958 [5,3,2,1,4] => 1382 [5,3,2,4,1] => 9234 [5,3,4,1,2] => 10544 [5,3,4,2,1] => 44062 [5,4,1,2,3] => 1634 [5,4,1,3,2] => 7160 [5,4,2,1,3] => 7160 [5,4,2,3,1] => 44062 [5,4,3,1,2] => 34266 [5,4,3,2,1] => 162482 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 1 [1,2,3,5,4,6] => 1 [1,2,3,5,6,4] => 2 [1,2,3,6,4,5] => 2 [1,2,3,6,5,4] => 5 [1,2,4,3,5,6] => 1 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 2 [1,2,4,5,6,3] => 6 [1,2,4,6,3,5] => 6 [1,2,4,6,5,3] => 18 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 6 [1,2,5,4,3,6] => 5 [1,2,5,4,6,3] => 18 [1,2,5,6,3,4] => 22 [1,2,5,6,4,3] => 62 [1,2,6,3,4,5] => 6 [1,2,6,3,5,4] => 18 [1,2,6,4,3,5] => 18 [1,2,6,4,5,3] => 73 [1,2,6,5,3,4] => 62 [1,2,6,5,4,3] => 210 [1,3,2,4,5,6] => 1 [1,3,2,4,6,5] => 2 [1,3,2,5,4,6] => 2 [1,3,2,5,6,4] => 6 [1,3,2,6,4,5] => 6 [1,3,2,6,5,4] => 18 [1,3,4,2,5,6] => 2 [1,3,4,2,6,5] => 6 [1,3,4,5,2,6] => 6 [1,3,4,5,6,2] => 24 [1,3,4,6,2,5] => 24 [1,3,4,6,5,2] => 86 [1,3,5,2,4,6] => 6 [1,3,5,2,6,4] => 24 [1,3,5,4,2,6] => 18 [1,3,5,4,6,2] => 86 [1,3,5,6,2,4] => 106 [1,3,5,6,4,2] => 352 [1,3,6,2,4,5] => 24 [1,3,6,2,5,4] => 86 [1,3,6,4,2,5] => 86 [1,3,6,4,5,2] => 418 [1,3,6,5,2,4] => 352 [1,3,6,5,4,2] => 1382 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 6 [1,4,2,5,3,6] => 6 [1,4,2,5,6,3] => 24 [1,4,2,6,3,5] => 24 [1,4,2,6,5,3] => 86 [1,4,3,2,5,6] => 5 [1,4,3,2,6,5] => 18 [1,4,3,5,2,6] => 18 [1,4,3,5,6,2] => 86 [1,4,3,6,2,5] => 86 [1,4,3,6,5,2] => 354 [1,4,5,2,3,6] => 22 [1,4,5,2,6,3] => 106 [1,4,5,3,2,6] => 62 [1,4,5,3,6,2] => 352 [1,4,5,6,2,3] => 508 [1,4,5,6,3,2] => 1634 [1,4,6,2,3,5] => 106 [1,4,6,2,5,3] => 462 [1,4,6,3,2,5] => 352 [1,4,6,3,5,2] => 1958 [1,4,6,5,2,3] => 1926 [1,4,6,5,3,2] => 7160 [1,5,2,3,4,6] => 6 [1,5,2,3,6,4] => 24 [1,5,2,4,3,6] => 18 [1,5,2,4,6,3] => 86 [1,5,2,6,3,4] => 106 [1,5,2,6,4,3] => 352 [1,5,3,2,4,6] => 18 [1,5,3,2,6,4] => 86 [1,5,3,4,2,6] => 73 [1,5,3,4,6,2] => 418 [1,5,3,6,2,4] => 462 [1,5,3,6,4,2] => 1958 [1,5,4,2,3,6] => 62 [1,5,4,2,6,3] => 352 [1,5,4,3,2,6] => 210 [1,5,4,3,6,2] => 1382 [1,5,4,6,2,3] => 1926 [1,5,4,6,3,2] => 7160 [1,5,6,2,3,4] => 508 [1,5,6,2,4,3] => 1926 [1,5,6,3,2,4] => 1926 [1,5,6,3,4,2] => 10544 [1,5,6,4,2,3] => 8022 [1,5,6,4,3,2] => 34266 [1,6,2,3,4,5] => 24 [1,6,2,3,5,4] => 86 [1,6,2,4,3,5] => 86 [1,6,2,4,5,3] => 418 [1,6,2,5,3,4] => 352 [1,6,2,5,4,3] => 1382 [1,6,3,2,4,5] => 86 [1,6,3,2,5,4] => 354 [1,6,3,4,2,5] => 418 [1,6,3,4,5,2] => 2381 [1,6,3,5,2,4] => 1958 [1,6,3,5,4,2] => 9234 [1,6,4,2,3,5] => 352 [1,6,4,2,5,3] => 1958 [1,6,4,3,2,5] => 1382 [1,6,4,3,5,2] => 9234 [1,6,4,5,2,3] => 10544 [1,6,4,5,3,2] => 44062 [1,6,5,2,3,4] => 1634 [1,6,5,2,4,3] => 7160 [1,6,5,3,2,4] => 7160 [1,6,5,3,4,2] => 44062 [1,6,5,4,2,3] => 34266 [1,6,5,4,3,2] => 162482 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 2 [2,1,3,5,4,6] => 2 [2,1,3,5,6,4] => 6 [2,1,3,6,4,5] => 6 [2,1,3,6,5,4] => 18 [2,1,4,3,5,6] => 2 [2,1,4,3,6,5] => 6 [2,1,4,5,3,6] => 6 [2,1,4,5,6,3] => 24 [2,1,4,6,3,5] => 24 [2,1,4,6,5,3] => 86 [2,1,5,3,4,6] => 6 [2,1,5,3,6,4] => 24 [2,1,5,4,3,6] => 18 [2,1,5,4,6,3] => 86 [2,1,5,6,3,4] => 106 [2,1,5,6,4,3] => 352 [2,1,6,3,4,5] => 24 [2,1,6,3,5,4] => 86 [2,1,6,4,3,5] => 86 [2,1,6,4,5,3] => 418 [2,1,6,5,3,4] => 352 [2,1,6,5,4,3] => 1382 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 6 [2,3,1,5,4,6] => 6 [2,3,1,5,6,4] => 24 [2,3,1,6,4,5] => 24 [2,3,1,6,5,4] => 86 [2,3,4,1,5,6] => 6 [2,3,4,1,6,5] => 24 [2,3,4,5,1,6] => 24 [2,3,4,5,6,1] => 120 [2,3,4,6,1,5] => 120 [2,3,4,6,5,1] => 504 [2,3,5,1,4,6] => 24 [2,3,5,1,6,4] => 120 [2,3,5,4,1,6] => 86 [2,3,5,4,6,1] => 504 [2,3,5,6,1,4] => 624 [2,3,5,6,4,1] => 2384 [2,3,6,1,4,5] => 120 [2,3,6,1,5,4] => 504 [2,3,6,4,1,5] => 504 [2,3,6,4,5,1] => 2854 [2,3,6,5,1,4] => 2384 [2,3,6,5,4,1] => 10632 [2,4,1,3,5,6] => 6 [2,4,1,3,6,5] => 24 [2,4,1,5,3,6] => 24 [2,4,1,5,6,3] => 120 [2,4,1,6,3,5] => 120 [2,4,1,6,5,3] => 504 [2,4,3,1,5,6] => 18 [2,4,3,1,6,5] => 86 [2,4,3,5,1,6] => 86 [2,4,3,5,6,1] => 504 [2,4,3,6,1,5] => 504 [2,4,3,6,5,1] => 2406 [2,4,5,1,3,6] => 106 [2,4,5,1,6,3] => 624 [2,4,5,3,1,6] => 352 [2,4,5,3,6,1] => 2384 [2,4,5,6,1,3] => 3468 [2,4,5,6,3,1] => 12608 [2,4,6,1,3,5] => 624 [2,4,6,1,5,3] => 3154 [2,4,6,3,1,5] => 2384 [2,4,6,3,5,1] => 15232 [2,4,6,5,1,3] => 14904 [2,4,6,5,3,1] => 62040 [2,5,1,3,4,6] => 24 [2,5,1,3,6,4] => 120 [2,5,1,4,3,6] => 86 [2,5,1,4,6,3] => 504 [2,5,1,6,3,4] => 624 [2,5,1,6,4,3] => 2384 [2,5,3,1,4,6] => 86 [2,5,3,1,6,4] => 504 [2,5,3,4,1,6] => 418 [2,5,3,4,6,1] => 2854 [2,5,3,6,1,4] => 3154 [2,5,3,6,4,1] => 15232 [2,5,4,1,3,6] => 352 [2,5,4,1,6,3] => 2384 [2,5,4,3,1,6] => 1382 [2,5,4,3,6,1] => 10632 [2,5,4,6,1,3] => 14904 [2,5,4,6,3,1] => 62040 [2,5,6,1,3,4] => 3468 [2,5,6,1,4,3] => 14904 [2,5,6,3,1,4] => 14904 [2,5,6,3,4,1] => 92128 [2,5,6,4,1,3] => 69482 [2,5,6,4,3,1] => 329304 [2,6,1,3,4,5] => 120 [2,6,1,3,5,4] => 504 [2,6,1,4,3,5] => 504 [2,6,1,4,5,3] => 2854 [2,6,1,5,3,4] => 2384 [2,6,1,5,4,3] => 10632 [2,6,3,1,4,5] => 504 [2,6,3,1,5,4] => 2406 [2,6,3,4,1,5] => 2854 [2,6,3,4,5,1] => 18610 [2,6,3,5,1,4] => 15232 [2,6,3,5,4,1] => 80582 [2,6,4,1,3,5] => 2384 [2,6,4,1,5,3] => 15232 [2,6,4,3,1,5] => 10632 [2,6,4,3,5,1] => 80582 [2,6,4,5,1,3] => 92128 [2,6,4,5,3,1] => 426328 [2,6,5,1,3,4] => 12608 [2,6,5,1,4,3] => 62040 [2,6,5,3,1,4] => 62040 [2,6,5,3,4,1] => 426328 [2,6,5,4,1,3] => 329304 [2,6,5,4,3,1] => 1718598 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 6 [3,1,2,5,4,6] => 6 [3,1,2,5,6,4] => 24 [3,1,2,6,4,5] => 24 [3,1,2,6,5,4] => 86 [3,1,4,2,5,6] => 6 [3,1,4,2,6,5] => 24 [3,1,4,5,2,6] => 24 [3,1,4,5,6,2] => 120 [3,1,4,6,2,5] => 120 [3,1,4,6,5,2] => 504 [3,1,5,2,4,6] => 24 [3,1,5,2,6,4] => 120 [3,1,5,4,2,6] => 86 [3,1,5,4,6,2] => 504 [3,1,5,6,2,4] => 624 [3,1,5,6,4,2] => 2384 [3,1,6,2,4,5] => 120 [3,1,6,2,5,4] => 504 [3,1,6,4,2,5] => 504 [3,1,6,4,5,2] => 2854 [3,1,6,5,2,4] => 2384 [3,1,6,5,4,2] => 10632 [3,2,1,4,5,6] => 5 [3,2,1,4,6,5] => 18 [3,2,1,5,4,6] => 18 [3,2,1,5,6,4] => 86 [3,2,1,6,4,5] => 86 [3,2,1,6,5,4] => 354 [3,2,4,1,5,6] => 18 [3,2,4,1,6,5] => 86 [3,2,4,5,1,6] => 86 [3,2,4,5,6,1] => 504 [3,2,4,6,1,5] => 504 [3,2,4,6,5,1] => 2406 [3,2,5,1,4,6] => 86 [3,2,5,1,6,4] => 504 [3,2,5,4,1,6] => 354 [3,2,5,4,6,1] => 2406 [3,2,5,6,1,4] => 2986 [3,2,5,6,4,1] => 12800 [3,2,6,1,4,5] => 504 [3,2,6,1,5,4] => 2406 [3,2,6,4,1,5] => 2406 [3,2,6,4,5,1] => 15410 [3,2,6,5,1,4] => 12800 [3,2,6,5,4,1] => 63510 [3,4,1,2,5,6] => 22 [3,4,1,2,6,5] => 106 [3,4,1,5,2,6] => 106 [3,4,1,5,6,2] => 624 [3,4,1,6,2,5] => 624 [3,4,1,6,5,2] => 2986 [3,4,2,1,5,6] => 62 [3,4,2,1,6,5] => 352 [3,4,2,5,1,6] => 352 [3,4,2,5,6,1] => 2384 [3,4,2,6,1,5] => 2384 [3,4,2,6,5,1] => 12800 [3,4,5,1,2,6] => 508 [3,4,5,1,6,2] => 3468 [3,4,5,2,1,6] => 1634 [3,4,5,2,6,1] => 12608 [3,4,5,6,1,2] => 20944 [3,4,5,6,2,1] => 74024 [3,4,6,1,2,5] => 3468 [3,4,6,1,5,2] => 20356 [3,4,6,2,1,5] => 12608 [3,4,6,2,5,1] => 90002 [3,4,6,5,1,2] => 100380 [3,4,6,5,2,1] => 400224 [3,5,1,2,4,6] => 106 [3,5,1,2,6,4] => 624 [3,5,1,4,2,6] => 462 [3,5,1,4,6,2] => 3154 [3,5,1,6,2,4] => 3774 [3,5,1,6,4,2] => 16832 [3,5,2,1,4,6] => 352 [3,5,2,1,6,4] => 2384 [3,5,2,4,1,6] => 1958 [3,5,2,4,6,1] => 15232 [3,5,2,6,1,4] => 16832 [3,5,2,6,4,1] => 90456 [3,5,4,1,2,6] => 1926 [3,5,4,1,6,2] => 14904 [3,5,4,2,1,6] => 7160 [3,5,4,2,6,1] => 62040 [3,5,4,6,1,2] => 99744 [3,5,4,6,2,1] => 398456 [3,5,6,1,2,4] => 21736 [3,5,6,1,4,2] => 110764 [3,5,6,2,1,4] => 87676 [3,5,6,2,4,1] => 598728 [3,5,6,4,1,2] => 512684 [3,5,6,4,2,1] => 2300762 [3,6,1,2,4,5] => 624 [3,6,1,2,5,4] => 2986 [3,6,1,4,2,5] => 3154 [3,6,1,4,5,2] => 20374 [3,6,1,5,2,4] => 16832 [3,6,1,5,4,2] => 85802 [3,6,2,1,4,5] => 2384 [3,6,2,1,5,4] => 12800 [3,6,2,4,1,5] => 15232 [3,6,2,4,5,1] => 110878 [3,6,2,5,1,4] => 90456 [3,6,2,5,4,1] => 527840 [3,6,4,1,2,5] => 14904 [3,6,4,1,5,2] => 108326 [3,6,4,2,1,5] => 62040 [3,6,4,2,5,1] => 521224 [3,6,4,5,1,2] => 683144 [3,6,4,5,2,1] => 3000024 [3,6,5,1,2,4] => 87676 [3,6,5,1,4,2] => 506992 [3,6,5,2,1,4] => 399248 [3,6,5,2,4,1] => 3013576 [3,6,5,4,1,2] => 2651262 [3,6,5,4,2,1] => 12996712 [4,1,2,3,5,6] => 6 [4,1,2,3,6,5] => 24 [4,1,2,5,3,6] => 24 [4,1,2,5,6,3] => 120 [4,1,2,6,3,5] => 120 [4,1,2,6,5,3] => 504 [4,1,3,2,5,6] => 18 [4,1,3,2,6,5] => 86 [4,1,3,5,2,6] => 86 [4,1,3,5,6,2] => 504 [4,1,3,6,2,5] => 504 [4,1,3,6,5,2] => 2406 [4,1,5,2,3,6] => 106 [4,1,5,2,6,3] => 624 [4,1,5,3,2,6] => 352 [4,1,5,3,6,2] => 2384 [4,1,5,6,2,3] => 3468 [4,1,5,6,3,2] => 12608 [4,1,6,2,3,5] => 624 [4,1,6,2,5,3] => 3154 [4,1,6,3,2,5] => 2384 [4,1,6,3,5,2] => 15232 [4,1,6,5,2,3] => 14904 [4,1,6,5,3,2] => 62040 [4,2,1,3,5,6] => 18 [4,2,1,3,6,5] => 86 [4,2,1,5,3,6] => 86 [4,2,1,5,6,3] => 504 [4,2,1,6,3,5] => 504 [4,2,1,6,5,3] => 2406 [4,2,3,1,5,6] => 73 [4,2,3,1,6,5] => 418 [4,2,3,5,1,6] => 418 [4,2,3,5,6,1] => 2854 [4,2,3,6,1,5] => 2854 [4,2,3,6,5,1] => 15410 [4,2,5,1,3,6] => 462 [4,2,5,1,6,3] => 3154 [4,2,5,3,1,6] => 1958 [4,2,5,3,6,1] => 15232 [4,2,5,6,1,3] => 20356 [4,2,5,6,3,1] => 90002 [4,2,6,1,3,5] => 3154 [4,2,6,1,5,3] => 17574 [4,2,6,3,1,5] => 15232 [4,2,6,3,5,1] => 109358 [4,2,6,5,1,3] => 96902 [4,2,6,5,3,1] => 490008 [4,3,1,2,5,6] => 62 [4,3,1,2,6,5] => 352 [4,3,1,5,2,6] => 352 [4,3,1,5,6,2] => 2384 [4,3,1,6,2,5] => 2384 [4,3,1,6,5,2] => 12800 [4,3,2,1,5,6] => 210 [4,3,2,1,6,5] => 1382 [4,3,2,5,1,6] => 1382 [4,3,2,5,6,1] => 10632 [4,3,2,6,1,5] => 10632 [4,3,2,6,5,1] => 63510 [4,3,5,1,2,6] => 1926 [4,3,5,1,6,2] => 14904 [4,3,5,2,1,6] => 7160 [4,3,5,2,6,1] => 62040 [4,3,5,6,1,2] => 100380 [4,3,5,6,2,1] => 400224 [4,3,6,1,2,5] => 14904 [4,3,6,1,5,2] => 96902 [4,3,6,2,1,5] => 62040 [4,3,6,2,5,1] => 490008 [4,3,6,5,1,2] => 526176 [4,3,6,5,2,1] => 2358416 [4,5,1,2,3,6] => 508 [4,5,1,2,6,3] => 3468 [4,5,1,3,2,6] => 1926 [4,5,1,3,6,2] => 14904 [4,5,1,6,2,3] => 21736 [4,5,1,6,3,2] => 87676 [4,5,2,1,3,6] => 1926 [4,5,2,1,6,3] => 14904 [4,5,2,3,1,6] => 10544 [4,5,2,3,6,1] => 92128 [4,5,2,6,1,3] => 110764 [4,5,2,6,3,1] => 598728 [4,5,3,1,2,6] => 8022 [4,5,3,1,6,2] => 69482 [4,5,3,2,1,6] => 34266 [4,5,3,2,6,1] => 329304 [4,5,3,6,1,2] => 512684 [4,5,3,6,2,1] => 2300762 [4,5,6,1,2,3] => 136706 [4,5,6,1,3,2] => 606384 [4,5,6,2,1,3] => 606384 [4,5,6,2,3,1] => 4050488 [4,5,6,3,1,2] => 2845672 [4,5,6,3,2,1] => 14292656 [4,6,1,2,3,5] => 3468 [4,6,1,2,5,3] => 20356 [4,6,1,3,2,5] => 14904 [4,6,1,3,5,2] => 108326 [4,6,1,5,2,3] => 110764 [4,6,1,5,3,2] => 506992 [4,6,2,1,3,5] => 14904 [4,6,2,1,5,3] => 96902 [4,6,2,3,1,5] => 92128 [4,6,2,3,5,1] => 753904 [4,6,2,5,1,3] => 692928 [4,6,2,5,3,1] => 4022640 [4,6,3,1,2,5] => 69482 [4,6,3,1,5,2] => 556686 [4,6,3,2,1,5] => 329304 [4,6,3,2,5,1] => 3035178 [4,6,3,5,1,2] => 3833302 [4,6,3,5,2,1] => 18816048 [4,6,5,1,2,3] => 606384 [4,6,5,1,3,2] => 3001406 [4,6,5,2,1,3] => 3019208 [4,6,5,2,3,1] => 22018344 [4,6,5,3,1,2] => 15762128 [4,6,5,3,2,1] => 86110376 [5,1,2,3,4,6] => 24 [5,1,2,3,6,4] => 120 [5,1,2,4,3,6] => 86 [5,1,2,4,6,3] => 504 [5,1,2,6,3,4] => 624 [5,1,2,6,4,3] => 2384 [5,1,3,2,4,6] => 86 [5,1,3,2,6,4] => 504 [5,1,3,4,2,6] => 418 [5,1,3,4,6,2] => 2854 [5,1,3,6,2,4] => 3154 [5,1,3,6,4,2] => 15232 [5,1,4,2,3,6] => 352 [5,1,4,2,6,3] => 2384 [5,1,4,3,2,6] => 1382 [5,1,4,3,6,2] => 10632 [5,1,4,6,2,3] => 14904 [5,1,4,6,3,2] => 62040 [5,1,6,2,3,4] => 3468 [5,1,6,2,4,3] => 14904 [5,1,6,3,2,4] => 14904 [5,1,6,3,4,2] => 92128 [5,1,6,4,2,3] => 69482 [5,1,6,4,3,2] => 329304 [5,2,1,3,4,6] => 86 [5,2,1,3,6,4] => 504 [5,2,1,4,3,6] => 354 [5,2,1,4,6,3] => 2406 [5,2,1,6,3,4] => 2986 [5,2,1,6,4,3] => 12800 [5,2,3,1,4,6] => 418 [5,2,3,1,6,4] => 2854 [5,2,3,4,1,6] => 2381 [5,2,3,4,6,1] => 18610 [5,2,3,6,1,4] => 20374 [5,2,3,6,4,1] => 110878 [5,2,4,1,3,6] => 1958 [5,2,4,1,6,3] => 15232 [5,2,4,3,1,6] => 9234 [5,2,4,3,6,1] => 80582 [5,2,4,6,1,3] => 108326 [5,2,4,6,3,1] => 521224 [5,2,6,1,3,4] => 20356 [5,2,6,1,4,3] => 96902 [5,2,6,3,1,4] => 108326 [5,2,6,3,4,1] => 753904 [5,2,6,4,1,3] => 556686 [5,2,6,4,3,1] => 3035178 [5,3,1,2,4,6] => 352 [5,3,1,2,6,4] => 2384 [5,3,1,4,2,6] => 1958 [5,3,1,4,6,2] => 15232 [5,3,1,6,2,4] => 16832 [5,3,1,6,4,2] => 90456 [5,3,2,1,4,6] => 1382 [5,3,2,1,6,4] => 10632 [5,3,2,4,1,6] => 9234 [5,3,2,4,6,1] => 80582 [5,3,2,6,1,4] => 85802 [5,3,2,6,4,1] => 527840 [5,3,4,1,2,6] => 10544 [5,3,4,1,6,2] => 92128 [5,3,4,2,1,6] => 44062 [5,3,4,2,6,1] => 426328 [5,3,4,6,1,2] => 683144 [5,3,4,6,2,1] => 3000024 [5,3,6,1,2,4] => 110764 [5,3,6,1,4,2] => 692928 [5,3,6,2,1,4] => 506992 [5,3,6,2,4,1] => 4022640 [5,3,6,4,1,2] => 3833302 [5,3,6,4,2,1] => 18816048 [5,4,1,2,3,6] => 1634 [5,4,1,2,6,3] => 12608 [5,4,1,3,2,6] => 7160 [5,4,1,3,6,2] => 62040 [5,4,1,6,2,3] => 87676 [5,4,1,6,3,2] => 399248 [5,4,2,1,3,6] => 7160 [5,4,2,1,6,3] => 62040 [5,4,2,3,1,6] => 44062 [5,4,2,3,6,1] => 426328 [5,4,2,6,1,3] => 506992 [5,4,2,6,3,1] => 3013576 [5,4,3,1,2,6] => 34266 [5,4,3,1,6,2] => 329304 [5,4,3,2,1,6] => 162482 [5,4,3,2,6,1] => 1718598 [5,4,3,6,1,2] => 2651262 [5,4,3,6,2,1] => 12996712 [5,4,6,1,2,3] => 606384 [5,4,6,1,3,2] => 3019208 [5,4,6,2,1,3] => 3001406 [5,4,6,2,3,1] => 22018344 [5,4,6,3,1,2] => 15762128 [5,4,6,3,2,1] => 86110376 [5,6,1,2,3,4] => 20944 [5,6,1,2,4,3] => 100380 [5,6,1,3,2,4] => 99744 [5,6,1,3,4,2] => 683144 [5,6,1,4,2,3] => 512684 [5,6,1,4,3,2] => 2651262 [5,6,2,1,3,4] => 100380 [5,6,2,1,4,3] => 526176 [5,6,2,3,1,4] => 683144 [5,6,2,3,4,1] => 5308656 [5,6,2,4,1,3] => 3833302 [5,6,2,4,3,1] => 23875224 [5,6,3,1,2,4] => 512684 [5,6,3,1,4,2] => 3833302 [5,6,3,2,1,4] => 2651262 [5,6,3,2,4,1] => 23875224 [5,6,3,4,1,2] => 25948726 [5,6,3,4,2,1] => 138388118 [5,6,4,1,2,3] => 2845672 [5,6,4,1,3,2] => 15762128 [5,6,4,2,1,3] => 15762128 [5,6,4,2,3,1] => 125228144 [5,6,4,3,1,2] => 91769546 [5,6,4,3,2,1] => 542024608 [6,1,2,3,4,5] => 120 [6,1,2,3,5,4] => 504 [6,1,2,4,3,5] => 504 [6,1,2,4,5,3] => 2854 [6,1,2,5,3,4] => 2384 [6,1,2,5,4,3] => 10632 [6,1,3,2,4,5] => 504 [6,1,3,2,5,4] => 2406 [6,1,3,4,2,5] => 2854 [6,1,3,4,5,2] => 18610 [6,1,3,5,2,4] => 15232 [6,1,3,5,4,2] => 80582 [6,1,4,2,3,5] => 2384 [6,1,4,2,5,3] => 15232 [6,1,4,3,2,5] => 10632 [6,1,4,3,5,2] => 80582 [6,1,4,5,2,3] => 92128 [6,1,4,5,3,2] => 426328 [6,1,5,2,3,4] => 12608 [6,1,5,2,4,3] => 62040 [6,1,5,3,2,4] => 62040 [6,1,5,3,4,2] => 426328 [6,1,5,4,2,3] => 329304 [6,1,5,4,3,2] => 1718598 [6,2,1,3,4,5] => 504 [6,2,1,3,5,4] => 2406 [6,2,1,4,3,5] => 2406 [6,2,1,4,5,3] => 15410 [6,2,1,5,3,4] => 12800 [6,2,1,5,4,3] => 63510 [6,2,3,1,4,5] => 2854 [6,2,3,1,5,4] => 15410 [6,2,3,4,1,5] => 18610 [6,2,3,4,5,1] => 136081 [6,2,3,5,1,4] => 110878 [6,2,3,5,4,1] => 651730 [6,2,4,1,3,5] => 15232 [6,2,4,1,5,3] => 109358 [6,2,4,3,1,5] => 80582 [6,2,4,3,5,1] => 681938 [6,2,4,5,1,3] => 753904 [6,2,4,5,3,1] => 3979998 [6,2,5,1,3,4] => 90002 [6,2,5,1,4,3] => 490008 [6,2,5,3,1,4] => 521224 [6,2,5,3,4,1] => 3979998 [6,2,5,4,1,3] => 3035178 [6,2,5,4,3,1] => 17788450 [6,3,1,2,4,5] => 2384 [6,3,1,2,5,4] => 12800 [6,3,1,4,2,5] => 15232 [6,3,1,4,5,2] => 110878 [6,3,1,5,2,4] => 90456 [6,3,1,5,4,2] => 527840 [6,3,2,1,4,5] => 10632 [6,3,2,1,5,4] => 63510 [6,3,2,4,1,5] => 80582 [6,3,2,4,5,1] => 651730 [6,3,2,5,1,4] => 527840 [6,3,2,5,4,1] => 3457350 [6,3,4,1,2,5] => 92128 [6,3,4,1,5,2] => 753904 [6,3,4,2,1,5] => 426328 [6,3,4,2,5,1] => 3979998 [6,3,4,5,1,2] => 5308656 [6,3,4,5,2,1] => 25359304 [6,3,5,1,2,4] => 598728 [6,3,5,1,4,2] => 4022640 [6,3,5,2,1,4] => 3013576 [6,3,5,2,4,1] => 25618632 [6,3,5,4,1,2] => 23875224 [6,3,5,4,2,1] => 126450110 [6,4,1,2,3,5] => 12608 [6,4,1,2,5,3] => 90002 [6,4,1,3,2,5] => 62040 [6,4,1,3,5,2] => 521224 [6,4,1,5,2,3] => 598728 [6,4,1,5,3,2] => 3013576 [6,4,2,1,3,5] => 62040 [6,4,2,1,5,3] => 490008 [6,4,2,3,1,5] => 426328 [6,4,2,3,5,1] => 3979998 [6,4,2,5,1,3] => 4022640 [6,4,2,5,3,1] => 25618632 [6,4,3,1,2,5] => 329304 [6,4,3,1,5,2] => 3035178 [6,4,3,2,1,5] => 1718598 [6,4,3,2,5,1] => 17788450 [6,4,3,5,1,2] => 23875224 [6,4,3,5,2,1] => 126450110 [6,4,5,1,2,3] => 4050488 [6,4,5,1,3,2] => 22018344 [6,4,5,2,1,3] => 22018344 [6,4,5,2,3,1] => 174937994 [6,4,5,3,1,2] => 125228144 [6,4,5,3,2,1] => 737498144 [6,5,1,2,3,4] => 74024 [6,5,1,2,4,3] => 400224 [6,5,1,3,2,4] => 398456 [6,5,1,3,4,2] => 3000024 [6,5,1,4,2,3] => 2300762 [6,5,1,4,3,2] => 12996712 [6,5,2,1,3,4] => 400224 [6,5,2,1,4,3] => 2358416 [6,5,2,3,1,4] => 3000024 [6,5,2,3,4,1] => 25359304 [6,5,2,4,1,3] => 18816048 [6,5,2,4,3,1] => 126450110 [6,5,3,1,2,4] => 2300762 [6,5,3,1,4,2] => 18816048 [6,5,3,2,1,4] => 12996712 [6,5,3,2,4,1] => 126450110 [6,5,3,4,1,2] => 138388118 [6,5,3,4,2,1] => 791921586 [6,5,4,1,2,3] => 14292656 [6,5,4,1,3,2] => 86110376 [6,5,4,2,1,3] => 86110376 [6,5,4,2,3,1] => 737498144 [6,5,4,3,1,2] => 542024608 ----------------------------------------------------------------------------- Created: Aug 28, 2017 at 16:39 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Aug 28, 2017 at 16:39 by Christian Stump