cp's OEIS Frontend

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.

%I A214430 #18 Jul 15 2020 00:20:18
%S A214430 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,
%T A214430 232,52,24,20,30,12,18,12,16,8,12,10,10,6,7,764,148,52,36,76,78,24,18,
%U A214430 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
%N 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.
%C A214430 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].
%H A214430 Kyle Petersen, <a href="/A214430/b214430.txt">Table of n, a(n) for n = 1..138</a>
%H A214430 T. Kyle Petersen and Bridget Eileen Tenner, <a href="http://arxiv.org/abs/1202.5319">How to write a permutation as a product of involutions (and why you might care)</a>, arXiv:1202.5319 [math.CO], 2012.
%e A214430 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.
%e A214430 Displayed as a triangle:
%e A214430 1
%e A214430 2, 2
%e A214430 4, 2, 3
%e A214430 10, 4, 6, 3, 4
%e A214430 26, 8, 6, 6, 6, 4, 5
%e A214430 76, 20, 12, 20, 12, 6, 12, 8, 8, 5, 6
%e A214430 232, 52, 24, 20, 30, 12, 18, 12, 16, 8, 12, 10, 10, 6, 7
%e A214430 764, 148, 52, 36, 76, 78, 24, 18, 24, 24, 36, 12, 20, 12, 20, 20, 10, 15, 12, 12, 7, 8
%p A214430 #For row n, we have the following.
%p A214430 P:=combinat[partition](n):
%p A214430 seq(add(abs(combinat[Chi](l, m)), l in P), m in P);
%Y A214430 Equal to A164341 for n<=7, row sums given in A214418. First column, corresponding to partition [1,1,...,1], is given by A000085.
%K A214430 nonn,tabf
%O A214430 1,2
%A A214430 _Kyle Petersen_, Jul 17 2012