A214430 Triangle read by rows, where T(n,m) is sum of the absolute values of the m-th column (in lexicographic ordering) in the character table of S_n.

1, 2, 2, 4, 2, 3, 10, 4, 6, 3, 4, 26, 8, 6, 6, 6, 4, 5, 76, 20, 12, 20, 12, 6, 12, 8, 8, 5, 6, 232, 52, 24, 20, 30, 12, 18, 12, 16, 8, 12, 10, 10, 6, 7, 764, 148, 52, 36, 76, 78, 24, 18, 24, 24, 36, 12, 20, 12, 20, 20, 10, 15, 12, 12, 7, 8, 2620, 460, 148, 76, 76, 208, 56, 32, 56, 40, 24, 54, 100, 28, 20, 20, 20, 20, 50

Offset: 1

Author

Kyle Petersen, Jul 17 2012

Keywords

• nonn
• tabf

Comments

Ordering on partitions is lexicographic, where partitions themselves are written in decreasing order, e.g., for n=5, the order is [1,1,1,1,1] < [2,1,1,1] < [2,2,1] < [3,1,1] < [3,2] < [4,1] < [5].

Examples

			The character table for S_3 is / 1 1 1 / 2 0 -1 / 1 -1 1 / and so T(3,1)=4, T(3,2)=2, and T(3,3)=3.
Displayed as a triangle:
1
2, 2
4, 2, 3
10, 4, 6, 3, 4
26, 8, 6, 6, 6, 4, 5
76, 20, 12, 20, 12, 6, 12, 8, 8, 5, 6
232, 52, 24, 20, 30, 12, 18, 12, 16, 8, 12, 10, 10, 6, 7
764, 148, 52, 36, 76, 78, 24, 18, 24, 24, 36, 12, 20, 12, 20, 20, 10, 15, 12, 12, 7, 8
		

Links

• Kyle Petersen, Table of n, a(n) for n = 1..138
• T. Kyle Petersen and Bridget Eileen Tenner, How to write a permutation as a product of involutions (and why you might care), arXiv:1202.5319 [math.CO], 2012.

Crossrefs

Equal to A164341 for n<=7, row sums given in A214418. First column, corresponding to partition [1,1,...,1], is given by A000085.

Programs

Maple

#For row n, we have the following.
P:=combinat[partition](n):
seq(add(abs(combinat[Chi](l, m)), l in P), m in P);