A321893 -id:A321893 - cp's OEIS frontend

A321892 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of f(v) in s(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 1, 0, 2, 5

Offset: 1

Gus Wiseman, Nov 20 2018

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).

			Triangle begins:
   1
   1
   0   1
   1   1
   0   0   1
   0   1   2
   0   0   0   0   1
   1   1   1
   0   1   0   1   2
   0   0   0   1   3
   0   0   0   0   0   0   1
   0   1   1   2   3
   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   1   4
   0   0   0   1   0   2   5
For example, row 15 gives: s(32) = f(221) + 2f(2111) + 5f(11111).

Wikipedia, Symmetric polynomial

Row sums are A321893.

Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A321742-A321765.

cp's OEIS Frontend

A321892 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of f(v) in s(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

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