Schur-Positivity in a Square
Keyword(s):
Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem. In this paper we study the Schur-positivity of a family of symmetric functions. Given a partition $\nu$, we denote by $\nu^c$ its complement in a square partition $(m^m)$. We conjecture a Schur-positivity criterion for symmetric functions of the form $s_{\mu'}s_{\mu^c}-s_{\nu'}s_{\nu^c}$, where $\nu$ is a partition of weight $|\mu|-1$ contained in $\mu$ and the complement of $\mu$ is taken in the same square partition as the complement of $\nu$. We prove the conjecture in many cases.
2015 ◽
Vol DMTCS Proceedings, 27th...
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1969 ◽
Vol 12
(5)
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pp. 615-623
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2012 ◽
Vol 22
(03)
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pp. 1250022
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1978 ◽
Vol 84
(1)
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pp. 1-3
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Keyword(s):
Keyword(s):
Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
1959 ◽
Vol 11
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pp. 383-396
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1972 ◽
Vol 15
(1)
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pp. 133-135
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