Rook polynomials in three and higher dimensions
نویسندگان
چکیده
منابع مشابه
Generalized Rook Polynomials and Orthogonal Polynomials
We consider several generalizations of rook polynomials. In particular we develop analogs of the theory of rook polynomials that are related to general Laguerre and Charlier polynomials in the same way that ordinary rook polynomials are related to simple Laguerre polynomials.
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Generalizing the notion of placing rooks on a Ferrers board leads to a new class of combinatorial models and a new class of rook polynomials. Connections are established with absolute Stirling numbers and permutations, Bessel polynomials, matchings, multiset permutations, hypergeometric functions, Abel polynomials and forests, and polynomial sequences of binomial type. Factorization and recipro...
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We study in this paper the set of magic squares and their relation with some restricted permutations. Résumé. Nous étudions dans cet article l’ensemble des carrés magiques et leur relation avec des permutations spéciales.
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In the 1920’s Artin defined the braid group, Bn, in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable from a braid by identifying the endpoints of each string. Because of this correspondence, the Jones and Alexander polynomials, two of the most ...
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We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reduc...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2013
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2013.6.35