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Identifier
Values
=>
Cc0002;cc-rep
[]=>1 [1]=>1 [2]=>1 [1,1]=>3 [3]=>1 [2,1]=>2 [1,1,1]=>10 [4]=>1 [3,1]=>2 [2,2]=>3 [2,1,1]=>7 [1,1,1,1]=>47 [5]=>1 [4,1]=>2 [3,2]=>2 [3,1,1]=>6 [2,2,1]=>6 [2,1,1,1]=>26 [1,1,1,1,1]=>246 [6]=>1 [5,1]=>2 [4,2]=>2 [4,1,1]=>6 [3,3]=>3 [3,2,1]=>6 [3,1,1,1]=>24 [2,2,2]=>10 [2,2,1,1]=>26 [2,1,1,1,1]=>138 [1,1,1,1,1,1]=>1602 [7]=>1 [6,1]=>2 [5,2]=>2 [5,1,1]=>6 [4,3]=>2 [4,2,1]=>5 [4,1,1,1]=>23 [3,3,1]=>6 [3,2,2]=>6 [3,2,1,1]=>20 [3,1,1,1,1]=>114 [2,2,2,1]=>23 [2,2,1,1,1]=>105 [2,1,1,1,1,1]=>767 [1,1,1,1,1,1,1]=>11481 [8]=>1 [7,1]=>2 [6,2]=>2 [6,1,1]=>6 [5,3]=>2 [5,2,1]=>5 [5,1,1,1]=>23 [4,4]=>3 [4,3,1]=>6 [4,2,2]=>7 [4,2,1,1]=>19 [4,1,1,1,1]=>111 [3,3,2]=>6 [3,3,1,1]=>22 [3,2,2,1]=>20 [3,2,1,1,1]=>90 [3,1,1,1,1,1]=>652 [2,2,2,2]=>47 [2,2,2,1,1]=>111 [2,2,1,1,1,1]=>599 [2,1,1,1,1,1,1]=>5295 [1,1,1,1,1,1,1,1]=>95503 [9]=>1 [8,1]=>2 [7,2]=>2 [7,1,1]=>6 [6,3]=>2 [6,2,1]=>5 [6,1,1,1]=>23 [5,4]=>2 [5,3,1]=>5 [5,2,2]=>6 [5,2,1,1]=>18 [5,1,1,1,1]=>110 [4,4,1]=>6 [4,3,2]=>5 [4,3,1,1]=>19 [4,2,2,1]=>18 [4,2,1,1,1]=>80 [4,1,1,1,1,1]=>622 [3,3,3]=>10 [3,3,2,1]=>21 [3,3,1,1,1]=>91 [3,2,2,2]=>23 [3,2,2,1,1]=>85 [3,2,1,1,1,1]=>471 [3,1,1,1,1,1,1]=>4285 [2,2,2,2,1]=>110 [2,2,2,1,1,1]=>512 [2,2,1,1,1,1,1]=>3586 [2,1,1,1,1,1,1,1]=>39468 [1,1,1,1,1,1,1,1,1]=>871030 [10]=>1 [9,1]=>2 [8,2]=>2 [8,1,1]=>6 [7,3]=>2 [7,2,1]=>5 [7,1,1,1]=>23 [6,4]=>2 [6,3,1]=>5 [6,2,2]=>6 [6,2,1,1]=>18 [6,1,1,1,1]=>110 [5,5]=>3 [5,4,1]=>6 [5,3,2]=>6 [5,3,1,1]=>18 [5,2,2,1]=>18 [5,2,1,1,1]=>78 [5,1,1,1,1,1]=>618 [4,4,2]=>6 [4,4,1,1]=>22 [4,3,3]=>6 [4,3,2,1]=>18 [4,3,1,1,1]=>84 [4,2,2,2]=>26 [4,2,2,1,1]=>78 [4,2,1,1,1,1]=>426 [4,1,1,1,1,1,1]=>4086 [3,3,3,1]=>23 [3,3,2,2]=>22 [3,3,2,1,1]=>82 [3,3,1,1,1,1]=>470 [3,2,2,2,1]=>86 [3,2,2,1,1,1]=>412 [3,2,1,1,1,1,1]=>2866 [3,1,1,1,1,1,1,1]=>32048 [2,2,2,2,2]=>246 [2,2,2,2,1,1]=>582 [2,2,2,1,1,1,1]=>3134 [2,2,1,1,1,1,1,1]=>26038 [2,1,1,1,1,1,1,1,1]=>340198 [1,1,1,1,1,1,1,1,1,1]=>8879558 [11]=>1 [10,1]=>2 [9,2]=>2 [9,1,1]=>6 [8,3]=>2 [8,2,1]=>5 [8,1,1,1]=>23 [7,4]=>2 [7,3,1]=>5 [7,2,2]=>6 [7,2,1,1]=>18 [7,1,1,1,1]=>110 [6,5]=>2 [6,4,1]=>5 [6,3,2]=>5 [6,3,1,1]=>17 [6,2,2,1]=>17 [6,2,1,1,1]=>77 [6,1,1,1,1,1]=>617 [5,5,1]=>6 [5,4,2]=>5 [5,4,1,1]=>19 [5,3,3]=>6 [5,3,2,1]=>17 [5,3,1,1,1]=>75 [5,2,2,2]=>23 [5,2,2,1,1]=>73 [5,2,1,1,1,1]=>407 [5,1,1,1,1,1,1]=>4041 [4,4,3]=>6 [4,4,2,1]=>17 [4,4,1,1,1]=>87 [4,3,3,1]=>19 [4,3,2,2]=>18 [4,3,2,1,1]=>70 [4,3,1,1,1,1]=>418 [4,2,2,2,1]=>77 [4,2,2,1,1,1]=>363 [4,2,1,1,1,1,1]=>2545 [4,1,1,1,1,1,1,1]=>30319 [3,3,3,2]=>23 [3,3,3,1,1]=>87 [3,3,2,2,1]=>79 [3,3,2,1,1,1]=>383 [3,3,1,1,1,1,1]=>2751 [3,2,2,2,2]=>110 [3,2,2,2,1,1]=>398 [3,2,2,1,1,1,1]=>2326 [3,2,1,1,1,1,1,1]=>19742 [3,1,1,1,1,1,1,1,1]=>268350 [2,2,2,2,2,1]=>617 [2,2,2,2,1,1,1]=>2855 [2,2,2,1,1,1,1,1]=>19853 [2,2,1,1,1,1,1,1,1]=>201403 [2,1,1,1,1,1,1,1,1,1]=>3166097 [1,1,1,1,1,1,1,1,1,1,1]=>98329551 [12]=>1 [11,1]=>2 [10,2]=>2 [10,1,1]=>6 [9,3]=>2 [9,2,1]=>5 [9,1,1,1]=>23 [8,4]=>2 [8,3,1]=>5 [8,2,2]=>6 [8,2,1,1]=>18 [8,1,1,1,1]=>110 [7,5]=>2 [7,4,1]=>5 [7,3,2]=>5 [7,3,1,1]=>17 [7,2,2,1]=>17 [7,2,1,1,1]=>77 [7,1,1,1,1,1]=>617 [6,6]=>3 [6,5,1]=>6 [6,4,2]=>6 [6,4,1,1]=>18 [6,3,3]=>7 [6,3,2,1]=>17 [6,3,1,1,1]=>73 [6,2,2,2]=>24 [6,2,2,1,1]=>72 [6,2,1,1,1,1]=>404 [6,1,1,1,1,1,1]=>4036 [5,5,2]=>6 [5,5,1,1]=>22 [5,4,3]=>5 [5,4,2,1]=>17 [5,4,1,1,1]=>83 [5,3,3,1]=>18 [5,3,2,2]=>19 [5,3,2,1,1]=>69 [5,3,1,1,1,1]=>387 [5,2,2,2,1]=>75 [5,2,2,1,1,1]=>349 [5,2,1,1,1,1,1]=>2451 [5,1,1,1,1,1,1,1]=>29997 [4,4,4]=>10 [4,4,3,1]=>21 [4,4,2,2]=>26 [4,4,2,1,1]=>74 [4,4,1,1,1,1]=>450 [4,3,3,2]=>18 [4,3,3,1,1]=>78 [4,3,2,2,1]=>73 [4,3,2,1,1,1]=>345 [4,3,1,1,1,1,1]=>2505 [4,2,2,2,2]=>138 [4,2,2,2,1,1]=>378 [4,2,2,1,1,1,1]=>2098 [4,2,1,1,1,1,1,1]=>17682 [4,1,1,1,1,1,1,1,1]=>253818 [3,3,3,3]=>47 [3,3,3,2,1]=>95 [3,3,3,1,1,1]=>419 [3,3,2,2,2]=>88 [3,3,2,2,1,1]=>392 [3,3,2,1,1,1,1]=>2204 [3,3,1,1,1,1,1,1]=>18908 [3,2,2,2,2,1]=>437 [3,2,2,2,1,1,1]=>2233 [3,2,2,1,1,1,1,1]=>15389 [3,2,1,1,1,1,1,1,1]=>154649 [3,1,1,1,1,1,1,1,1,1]=>2501957 [2,2,2,2,2,2]=>1602 [2,2,2,2,2,1,1]=>3546 [2,2,2,2,1,1,1,1]=>19274 [2,2,2,1,1,1,1,1,1]=>154210 [2,2,1,1,1,1,1,1,1,1]=>1807634 [2,1,1,1,1,1,1,1,1,1,1]=>33022346 [1,1,1,1,1,1,1,1,1,1,1,1]=>1191578522
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Description
The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions.
For example, $p_{22} = 2m_{22} + m_4$, so the statistic on the partition $22$ is 3.
Code
def statistic(mu):
    m = SymmetricFunctions(ZZ).m()
    p = SymmetricFunctions(ZZ).p()
    return sum(coeff for _, coeff in m(p(mu)))
Created
May 20, 2017 at 17:57 by Martin Rubey
Updated
Oct 31, 2017 at 08:07 by Martin Rubey