A321930 Tetrangle where T(n,H(u),H(v)) is the coefficient of s(v) in f(u), where u and v are integer partitions of n, H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.
1, -1, 1, 1, 0, 1, -1, 1, -2, 1, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 1, -1, 0, 0, 2, -1, -1, 1, 0, -3, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 1, -2, 1, 1, -1, -1, 1, 0, -2, 2, -1, 1, -1, 0, 0, 3, -2, 1, 0, 0, 0, 0, 3, -1, -1, 0, 1, 0, 0, -4, 1, 0, 0, 0, 0
Offset: 1
Examples
Tetrangle begins (zeros not shown): (1): 1 . (2): -1 1 (11): 1 . (3): 1 -1 1 (21): -2 1 (111): 1 . (4): -1 1 -1 1 (22): 1 1 -1 (31): 2 -1 -1 1 (211): -3 1 (1111): 1 . (5): 1 -1 1 -1 1 (41): -2 1 1 -1 -1 1 (32): -2 2 -1 1 -1 (221): 3 -2 1 (311): 3 -1 -1 1 (2111): -4 1 (11111): 1 For example, row 14 gives: f(32) = -2s(5) - s(32) + 2s(41) + s(221) - s(311).
Links
- Wikipedia, Symmetric polynomial
Comments