A321920 Tetrangle where T(n,H(u),H(v)) is the coefficient of e(v) in s(u), where u and v are integer partitions of n, H is Heinz number, e is elementary symmetric functions, and s is Schur functions.
1, -1, 1, 1, 0, 1, -2, 1, -1, 1, 0, 1, 0, 0, -1, 1, 2, -3, 1, 0, 1, -1, 0, 0, 1, -1, -1, 1, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, -2, -2, 3, 3, -4, 1, -1, 1, 2, -2, -1, 1, 0, 0, 1, -1, 1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, -1, 1, 0, 0, 0, 0
Offset: 1
Examples
Tetrangle begins (zeroes not shown): (1): 1 . (2): -1 1 (11): 1 . (3): 1 -2 1 (21): -1 1 (111): 1 . (4): -1 1 2 -3 1 (22): 1 -1 (31): 1 -1 -1 1 (211): -1 1 (1111): 1 . (5): 1 -2 -2 3 3 -4 1 (41): -1 1 2 -2 -1 1 (32): 1 -1 1 -1 (221): -1 1 (311): 1 -1 -1 1 (2111): -1 1 (11111): 1 For example, row 14 gives: s(32) = -e(32) + e(41) + e(221) - e(311).
Links
- Wikipedia, Symmetric polynomial
Comments