login
A321755
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of e(v) in s(u), where H is Heinz number, e is elementary symmetric functions, and s is Schur functions.
1
1, 1, -1, 1, 1, 0, 1, -2, 1, -1, 1, 0, -1, 1, 2, -3, 1, 1, 0, 0, 0, 1, -1, 0, 0, 1, -1, -1, 1, 0, 1, -2, -2, 3, 3, -4, 1, -1, 0, 1, 0, 0, -1, 2, 2, 1, -1, -3, -6, 6, 4, -5, 1, -1, 1, 2, -2, -1, 1, 0, 0, 1, -1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 1, -2, -2, -2, 6, 3, 3
OFFSET
1,8
COMMENTS
Row n has length A000041(A056239(n)).
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Triangle begins:
1
1
-1 1
1 0
1 -2 1
-1 1 0
-1 1 2 -3 1
1 0 0
0 1 -1 0 0
1 -1 -1 1 0
1 -2 -2 3 3 -4 1
-1 0 1 0 0
-1 2 2 1 -1 -3 -6 6 4 -5 1
-1 1 2 -2 -1 1 0
0 1 -1 1 -1 0 0
1 0 0 0 0
1 -2 -2 -2 6 3 3 3 -4 -4 -12 10 5 -6 1
0 -1 1 0 0 0 0
For example, row 14 gives: s(41) = -e(5) + 2e(32) + e(41) - 2e(221) - e(311) + e(2111).
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved