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A321758
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of h(v) in s(u), where H is Heinz number, h is homogeneous symmetric functions, and s is Schur functions.
1
1, 1, 1, 0, -1, 1, 1, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 1, -2, 1, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 2, -3, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1,19
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 0
-1 1
1 0 0
-1 1 0
1 0 0 0 0
1 -2 1
0 1 -1 0 0
-1 0 1 0 0
1 0 0 0 0 0 0
1 -1 -1 1 0
1 0 0 0 0 0 0 0 0 0 0
-1 1 0 0 0 0 0
0 -1 1 0 0 0 0
-1 1 2 -3 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 -1 1 -1 0 0
For example, row 18 gives: s(221) = -h(32) + h(41) + h(221) - h(311).
KEYWORD
sign,tabf
AUTHOR
Gus Wiseman, Nov 20 2018
STATUS
approved