A321765 - OEIS

A321765

Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in p(u), where H is Heinz number, p is power sum symmetric functions, and s is Schur functions.

1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 2, 1, 1, 2, -1, -1, 1, 1, -1, 0, 0, 1, 1, -1, 0, 0, 1, -1, 1, 1, 0, 1, -1, -1, 1, 0, -1, 0, 0, 1, 0, 0, -1, 1, -1, 1, 0, -1, 1, 0, 0, -1

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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).

LINKS

Table of n, a(n) for n=1..60.

Wikipedia, Symmetric polynomial

EXAMPLE

Triangle begins:

1 -1

1 1

1 -1 1

1 0 -1

1 0 -1 1 -1

1 2 1

1 2 -1 -1 1

1 -1 0 0 1

1 -1 0 0 1 -1 1

1 0 1 -1 -1

1 0 -1 0 0 1 0 0 -1 1 -1

1 0 -1 1 0 0 -1

For example, row 12 gives: p(211) = s(4) + s(31) - s(211) - s(1111).

CROSSREFS

Row sums are A317554.

Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A296561, A300121, A304438, A317552, A317554, A321742-A321765.

Sequence in context: A015776 A176047 A067461 * A328310 A136673 A283149

Adjacent sequences: A321762 A321763 A321764 * A321766 A321767 A321768

KEYWORD

sign,tabf,more

AUTHOR

Gus Wiseman, Nov 20 2018

STATUS

approved