|
|
A321931
|
|
Tetrangle where T(n,H(u),H(v)) is the coefficient of p(v) in M(u), where u and v are integer partitions of n, H is Heinz number, p is power sum symmetric functions, and M is augmented monomial symmetric functions.
|
|
4
|
|
|
1, 1, 0, -1, 1, 1, 0, 0, -1, 1, 0, 2, -3, 1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, 2, -1, -2, 1, 0, -6, 3, 8, -6, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 2, -1, -2, 1, 0, 0, 0, 2, -2, -1, 0, 1, 0, 0, -6, 6, 5, -3, -3, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,12
|
|
COMMENTS
|
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
The augmented monomial symmetric functions are given by M(y) = c(y) * m(y) where c(y) = Product_i (y)_i! where (y)_i is the number of i's in y and m is monomial symmetric functions.
|
|
LINKS
|
|
|
EXAMPLE
|
Tetrangle begins (zeros not shown):
(1): 1
.
(2): 1
(11): -1 1
.
(3): 1
(21): -1 1
(111): 2 -3 1
.
(4): 1
(22): -1 1
(31): -1 1
(211): 2 -1 -2 1
(1111): -6 3 8 -6 1
.
(5): 1
(41): -1 1
(32): -1 1
(221): 2 -1 -2 1
(311): 2 -2 -1 1
(2111): -6 6 5 -3 -3 1
(11111): 24 30 20 15 20 10 1
For example, row 14 gives: M(32) = -p(5) + p(32).
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|