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

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   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