A321759 -id:A321759 - cp's OEIS frontend

A321923 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in h(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and h is homogeneous symmetric functions.

1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 2, 3, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 3, 3, 2, 3, 1, 0, 1, 4, 5, 5, 6, 4

Offset: 1

Gus Wiseman, Nov 22 2018

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

			Tetrangle begins (zeroes not shown):
  (1): 1
.
  (2):  1
  (11): 1 1
.
  (3):   1
  (21):  1 1
  (111): 1 2 1
.
  (4):    1
  (22):   1 1 1
  (31):   1   1
  (211):  1 1 2 1
  (1111): 1 2 3 3 1
.
  (5):     1
  (41):    1 1
  (32):    1 1 1
  (221):   1 2 2 1 1
  (311):   1 2 1   1
  (2111):  1 3 3 2 3 1
  (11111): 1 4 5 5 6 4 1
For example, row 14 gives: h(32) = s(5) + s(32) + s(41).

Wikipedia, Symmetric polynomial

This is a regrouping of the triangle A321759.

Cf. A005651, A008480, A056239, A124794, A124795, A153452, A215366, A296188, A300121, A319191, A319193, A321912-A321935.

cp's OEIS Frontend

A321923 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in h(u), where u and v are integer partitions of n, H is Heinz number, s is Schur functions, and h is homogeneous symmetric functions.

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