A321924 Tetrangle where T(n,H(u),H(v)) is the coefficient of m(v) in s(u), where u and v are integer partitions of n, H is Heinz number, m is monomial symmetric functions, and s is Schur functions.

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

Offset: 1

Author

Gus Wiseman, Nov 22 2018

Keywords

• nonn
• tabf

Comments

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

Examples

			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 1
  (22):     1   1 2
  (31):     1 1 2 3
  (211):        1 3
  (1111):         1
.
  (5):     1 1 1 1 1 1 1
  (41):      1 1 2 2 3 4
  (32):        1 2 1 3 5
  (221):         1   2 5
  (311):         1 1 3 6
  (2111):            1 4
  (11111):             1
For example, row 14 gives: s(32) = m(32) + 2m(221) + m(311) + 3m(2111) + 5m(11111).
		

Links

• Wikipedia, Symmetric polynomial

Crossrefs

This is a regrouping of the triangle A321761.

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