2-adic valuations of certain ratios of products of factorials and applications

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dc.creatorFriedland, Shmuel
dc.creatorKrattenthaler, Christian
dc.date2005-08-25
dc.date2005-08-26
dc.date.accessioned2026-07-07T08:24:30Z
dc.date.available2026-07-07T08:24:30Z
dc.descriptionWe prove the conjecture of Falikman--Friedland--Loewy on the parity of the degrees of projective varieties of $n\times n$ complex symmetric matrices of rank at most $k$. We also characterize the parity of the degrees of projective varieties of $n\times n$ complex skew symmetric matrices of rank at most $2p$. We give recursive relations which determine the parity of the degrees of projective varieties of $m\times n$ complex matrices of rank at most $k$. In the case the degrees of these varieties are odd, we characterize the minimal dimensions of subspaces of $n\times n$ skew symmetric real matrices and of $m\times n$ real matrices containing a nonzero matrix of rank at most $k$. The parity questions studied here are also of combinatorial interest since they concern the parity of the number of plane partitions contained in a given box, on the one hand, and the parity of the number of symplectic tableaux of rectangular shape, on the other hand.
dc.descriptionLaTeX; 27 pages; author name corrected
dc.identifierhttps://arxiv.org/abs/math/0508498
dc.identifierhttp://arxiv.org/abs/math/0508498
dc.identifierLinear Algebra Appl. 426 (2007), 159-189.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136361
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subjectPrimary: 11A07, 15A03; Secondary: 14M12, 14P25, 15A30
dc.title2-adic valuations of certain ratios of products of factorials and applications
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