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
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
Programs
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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);
Comments