Identifier
Values
=>
Cc0002;cc-rep
[1]=>1
[2]=>5
[1,1]=>4
[3]=>37
[2,1]=>55
[1,1,1]=>23
[4]=>405
[3,1]=>587
[2,2]=>284
[2,1,1]=>712
[1,1,1,1]=>206
[5]=>5251
[4,1]=>7501
[3,2]=>7151
[3,1,1]=>8949
[2,2,1]=>8719
[2,1,1,1]=>10103
[1,1,1,1,1]=>2247
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Description
The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition.
In other words, it is the sum of the coefficients in
$$(-1)^{|\lambda|-\ell(\lambda)}\nabla p_\lambda \vert_{q=1,t=1},$$
when expanded in the monomial basis.
Here, $\nabla$ is the linear operator on symmetric functions
where the modified Macdonald polynomials are eigenvectors. See the Sage documentation for definition and references http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/sf/sfa.html
In other words, it is the sum of the coefficients in
$$(-1)^{|\lambda|-\ell(\lambda)}\nabla p_\lambda \vert_{q=1,t=1},$$
when expanded in the monomial basis.
Here, $\nabla$ is the linear operator on symmetric functions
where the modified Macdonald polynomials are eigenvectors. See the Sage documentation for definition and references http://doc.sagemath.org/html/en/reference/combinat/sage/combinat/sf/sfa.html
References
[1] Bergeron, F., Garsia, A. M., Haiman, M., Tesler, G. Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions DOI:10.4310/maa.1999.v6.n3.a7
Created
Apr 13, 2020 at 21:26 by Per Alexandersson
Updated
Apr 13, 2020 at 21:26 by Per Alexandersson
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