|
|
A321765
|
|
Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in p(u), where H is Heinz number, p is power sum symmetric functions, and s is Schur functions.
|
|
40
|
|
|
1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 2, 1, 1, 2, -1, -1, 1, 1, -1, 0, 0, 1, 1, -1, 0, 0, 1, -1, 1, 1, 0, 1, -1, -1, 1, 0, -1, 0, 0, 1, 0, 0, -1, 1, -1, 1, 0, -1, 1, 0, 0, -1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,19
|
|
COMMENTS
|
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
1
1
1 -1
1 1
1 -1 1
1 0 -1
1 0 -1 1 -1
1 2 1
1 2 -1 -1 1
1 -1 0 0 1
1 -1 0 0 1 -1 1
1 0 1 -1 -1
1 0 -1 0 0 1 0 0 -1 1 -1
1 0 -1 1 0 0 -1
For example, row 12 gives: p(211) = s(4) + s(31) - s(211) - s(1111).
|
|
CROSSREFS
|
Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A296561, A300121, A304438, A317552, A317554, A321742-A321765.
|
|
KEYWORD
|
sign,tabf,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|