Identifier
Values
[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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