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A321930
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Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in f(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.
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0
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1, -1, 1, 1, 0, 1, -1, 1, -2, 1, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 1, -1, 0, 0, 2, -1, -1, 1, 0, -3, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, -2, 1, 1, -1, -1, 1, 0, -2, 2, -1, 1, -1, 0, 0, 3, -2, 1, 0, 0, 0, 0, 3, -1, -1, 0, 1, 0, 0, -4, 1, 0, 0, 0, 0
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OFFSET
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1,9
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COMMENTS
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The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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EXAMPLE
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Tetrangle begins (zeros not shown):
(1): 1
.
(2): -1 1
(11): 1
.
(3): 1 -1 1
(21): -2 1
(111): 1
.
(4): -1 1 -1 1
(22): 1 1 -1
(31): 2 -1 -1 1
(211): -3 1
(1111): 1
.
(5): 1 -1 1 -1 1
(41): -2 1 1 -1 -1 1
(32): -2 2 -1 1 -1
(221): 3 -2 1
(311): 3 -1 -1 1
(2111): -4 1
(11111): 1
For example, row 14 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).
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CROSSREFS
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This is a regrouping of the triangle A321894.
Cf. A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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