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A321925
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Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in m(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and m is monomial symmetric functions.
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1
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1, 1, -1, 0, 1, 1, -1, 1, 0, 1, -2, 0, 0, 1, 1, 0, -1, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1, -1, 2, 0, 0, 0, 1, -3, 0, 0, 0, 0, 1, 1, -1, 0, 0, 1, -1, 1, 0, 1, -1, 1, -1, 1, -2, 0, 0, 1, -1, -1, 2, -2, 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, -1, 1, -1, 3, 0, 0, 0, 0, 0, 1
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OFFSET
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1,11
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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 (zeroes not shown):
(1): 1
.
(2): 1 -1
(11): 1
.
(3): 1 -1 1
(21): 1 -2
(111): 1
.
(4): 1 -1 1 -1
(22): 1 -1 1
(31): -1 1 -1 2
(211): 1 -3
(1111): 1
.
(5): 1 -1 1 -1 1
(41): 1 -1 1 -1 1 -2
(32): 1 -1 -1 2 -2
(221): 1 -2 3
(311): -1 1 -1 3
(2111): 1 -4
(11111): 1
For example, row 14 gives: m(32) = s(32) - s(221) - s(311) + 2s(2111) - 2s(11111).
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CROSSREFS
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This is a regrouping of the triangle A321763.
Cf. A005651, 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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