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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St000532
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The total number of rook placements on a Ferrers board.
-----------------------------------------------------------------------------
References: [1] [[wikipedia:Rook_polynomial]]
-----------------------------------------------------------------------------
Code:
def statistic(la):
return sum(matrix([[1]*p + [0]*(la[0]-p) for p in la]).rook_vector())
-----------------------------------------------------------------------------
Statistic values:
[] => 1
[1] => 2
[2] => 3
[1,1] => 3
[3] => 4
[2,1] => 5
[1,1,1] => 4
[4] => 5
[3,1] => 7
[2,2] => 7
[2,1,1] => 7
[1,1,1,1] => 5
[5] => 6
[4,1] => 9
[3,2] => 10
[3,1,1] => 10
[2,2,1] => 10
[2,1,1,1] => 9
[1,1,1,1,1] => 6
[6] => 7
[5,1] => 11
[4,2] => 13
[4,1,1] => 13
[3,3] => 13
[3,2,1] => 15
[3,1,1,1] => 13
[2,2,2] => 13
[2,2,1,1] => 13
[2,1,1,1,1] => 11
[1,1,1,1,1,1] => 7
[7] => 8
[6,1] => 13
[5,2] => 16
[5,1,1] => 16
[4,3] => 17
[4,2,1] => 20
[4,1,1,1] => 17
[3,3,1] => 20
[3,2,2] => 20
[3,2,1,1] => 20
[3,1,1,1,1] => 16
[2,2,2,1] => 17
[2,2,1,1,1] => 16
[2,1,1,1,1,1] => 13
[1,1,1,1,1,1,1] => 8
[8] => 9
[7,1] => 15
[6,2] => 19
[6,1,1] => 19
[5,3] => 21
[5,2,1] => 25
[5,1,1,1] => 21
[4,4] => 21
[4,3,1] => 27
[4,2,2] => 27
[4,2,1,1] => 27
[4,1,1,1,1] => 21
[3,3,2] => 27
[3,3,1,1] => 27
[3,2,2,1] => 27
[3,2,1,1,1] => 25
[3,1,1,1,1,1] => 19
[2,2,2,2] => 21
[2,2,2,1,1] => 21
[2,2,1,1,1,1] => 19
[2,1,1,1,1,1,1] => 15
[1,1,1,1,1,1,1,1] => 9
[9] => 10
[8,1] => 17
[7,2] => 22
[7,1,1] => 22
[6,3] => 25
[6,2,1] => 30
[6,1,1,1] => 25
[5,4] => 26
[5,3,1] => 34
[5,2,2] => 34
[5,2,1,1] => 34
[5,1,1,1,1] => 26
[4,4,1] => 34
[4,3,2] => 37
[4,3,1,1] => 37
[4,2,2,1] => 37
[4,2,1,1,1] => 34
[4,1,1,1,1,1] => 25
[3,3,3] => 34
[3,3,2,1] => 37
[3,3,1,1,1] => 34
[3,2,2,2] => 34
[3,2,2,1,1] => 34
[3,2,1,1,1,1] => 30
[3,1,1,1,1,1,1] => 22
[2,2,2,2,1] => 26
[2,2,2,1,1,1] => 25
[2,2,1,1,1,1,1] => 22
[2,1,1,1,1,1,1,1] => 17
[1,1,1,1,1,1,1,1,1] => 10
[10] => 11
[9,1] => 19
[8,2] => 25
[8,1,1] => 25
[7,3] => 29
[7,2,1] => 35
[7,1,1,1] => 29
[6,4] => 31
[6,3,1] => 41
[6,2,2] => 41
[6,2,1,1] => 41
[6,1,1,1,1] => 31
[5,5] => 31
[5,4,1] => 43
[5,3,2] => 47
[5,3,1,1] => 47
[5,2,2,1] => 47
[5,2,1,1,1] => 43
[5,1,1,1,1,1] => 31
[4,4,2] => 47
[4,4,1,1] => 47
[4,3,3] => 47
[4,3,2,1] => 52
[4,3,1,1,1] => 47
[4,2,2,2] => 47
[4,2,2,1,1] => 47
[4,2,1,1,1,1] => 41
[4,1,1,1,1,1,1] => 29
[3,3,3,1] => 47
[3,3,2,2] => 47
[3,3,2,1,1] => 47
[3,3,1,1,1,1] => 41
[3,2,2,2,1] => 43
[3,2,2,1,1,1] => 41
[3,2,1,1,1,1,1] => 35
[3,1,1,1,1,1,1,1] => 25
[2,2,2,2,2] => 31
[2,2,2,2,1,1] => 31
[2,2,2,1,1,1,1] => 29
[2,2,1,1,1,1,1,1] => 25
[2,1,1,1,1,1,1,1,1] => 19
[1,1,1,1,1,1,1,1,1,1] => 11
[11] => 12
[10,1] => 21
[9,2] => 28
[9,1,1] => 28
[8,3] => 33
[8,2,1] => 40
[8,1,1,1] => 33
[7,4] => 36
[7,3,1] => 48
[7,2,2] => 48
[7,2,1,1] => 48
[7,1,1,1,1] => 36
[6,5] => 37
[6,4,1] => 52
[6,3,2] => 57
[6,3,1,1] => 57
[6,2,2,1] => 57
[6,2,1,1,1] => 52
[6,1,1,1,1,1] => 37
[5,5,1] => 52
[5,4,2] => 60
[5,4,1,1] => 60
[5,3,3] => 60
[5,3,2,1] => 67
[5,3,1,1,1] => 60
[5,2,2,2] => 60
[5,2,2,1,1] => 60
[5,2,1,1,1,1] => 52
[5,1,1,1,1,1,1] => 36
[4,4,3] => 60
[4,4,2,1] => 67
[4,4,1,1,1] => 60
[4,3,3,1] => 67
[4,3,2,2] => 67
[4,3,2,1,1] => 67
[4,3,1,1,1,1] => 57
[4,2,2,2,1] => 60
[4,2,2,1,1,1] => 57
[4,2,1,1,1,1,1] => 48
[4,1,1,1,1,1,1,1] => 33
[3,3,3,2] => 60
[3,3,3,1,1] => 60
[3,3,2,2,1] => 60
[3,3,2,1,1,1] => 57
[3,3,1,1,1,1,1] => 48
[3,2,2,2,2] => 52
[3,2,2,2,1,1] => 52
[3,2,2,1,1,1,1] => 48
[3,2,1,1,1,1,1,1] => 40
[3,1,1,1,1,1,1,1,1] => 28
[2,2,2,2,2,1] => 37
[2,2,2,2,1,1,1] => 36
[2,2,2,1,1,1,1,1] => 33
[2,2,1,1,1,1,1,1,1] => 28
[2,1,1,1,1,1,1,1,1,1] => 21
[1,1,1,1,1,1,1,1,1,1,1] => 12
[12] => 13
[11,1] => 23
[10,2] => 31
[10,1,1] => 31
[9,3] => 37
[9,2,1] => 45
[9,1,1,1] => 37
[8,4] => 41
[8,3,1] => 55
[8,2,2] => 55
[8,2,1,1] => 55
[8,1,1,1,1] => 41
[7,5] => 43
[7,4,1] => 61
[7,3,2] => 67
[7,3,1,1] => 67
[7,2,2,1] => 67
[7,2,1,1,1] => 61
[7,1,1,1,1,1] => 43
[6,6] => 43
[6,5,1] => 63
[6,4,2] => 73
[6,4,1,1] => 73
[6,3,3] => 73
[6,3,2,1] => 82
[6,3,1,1,1] => 73
[6,2,2,2] => 73
[6,2,2,1,1] => 73
[6,2,1,1,1,1] => 63
[6,1,1,1,1,1,1] => 43
[5,5,2] => 73
[5,5,1,1] => 73
[5,4,3] => 77
[5,4,2,1] => 87
[5,4,1,1,1] => 77
[5,3,3,1] => 87
[5,3,2,2] => 87
[5,3,2,1,1] => 87
[5,3,1,1,1,1] => 73
[5,2,2,2,1] => 77
[5,2,2,1,1,1] => 73
[5,2,1,1,1,1,1] => 61
[5,1,1,1,1,1,1,1] => 41
[4,4,4] => 73
[4,4,3,1] => 87
[4,4,2,2] => 87
[4,4,2,1,1] => 87
[4,4,1,1,1,1] => 73
[4,3,3,2] => 87
[4,3,3,1,1] => 87
[4,3,2,2,1] => 87
[4,3,2,1,1,1] => 82
[4,3,1,1,1,1,1] => 67
[4,2,2,2,2] => 73
[4,2,2,2,1,1] => 73
[4,2,2,1,1,1,1] => 67
[4,2,1,1,1,1,1,1] => 55
[4,1,1,1,1,1,1,1,1] => 37
[3,3,3,3] => 73
[3,3,3,2,1] => 77
[3,3,3,1,1,1] => 73
[3,3,2,2,2] => 73
[3,3,2,2,1,1] => 73
[3,3,2,1,1,1,1] => 67
[3,3,1,1,1,1,1,1] => 55
[3,2,2,2,2,1] => 63
[3,2,2,2,1,1,1] => 61
[3,2,2,1,1,1,1,1] => 55
[3,2,1,1,1,1,1,1,1] => 45
[3,1,1,1,1,1,1,1,1,1] => 31
[2,2,2,2,2,2] => 43
[2,2,2,2,2,1,1] => 43
[2,2,2,2,1,1,1,1] => 41
[2,2,2,1,1,1,1,1,1] => 37
[2,2,1,1,1,1,1,1,1,1] => 31
[2,1,1,1,1,1,1,1,1,1,1] => 23
[1,1,1,1,1,1,1,1,1,1,1,1] => 13
[5,4,3,1] => 114
[5,4,2,2] => 114
[5,4,2,1,1] => 114
[5,3,3,2] => 114
[5,3,3,1,1] => 114
[5,3,2,2,1] => 114
[4,4,3,2] => 114
[4,4,3,1,1] => 114
[4,4,2,2,1] => 114
[4,3,3,2,1] => 114
[5,4,3,2] => 151
[5,4,3,1,1] => 151
[5,4,2,2,1] => 151
[5,3,3,2,1] => 151
[4,4,3,2,1] => 151
[5,4,3,2,1] => 203
-----------------------------------------------------------------------------
Created: Jun 10, 2016 at 23:59 by Martin Rubey
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Last Updated: Apr 26, 2018 at 07:39 by Martin Rubey