منابع مشابه
Generalized Rook Polynomials
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...
متن کاملGeneralized 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.
متن کاملMagic Squares, Rook Polynomials and Permutations
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.
متن کاملThe Alexander and Jones Polynomials Through Representations of Rook Algebras
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 ...
متن کاملFurther Investigations Involving Rook Polynomials With Only Real Zeros
We study the zeros of two families of polynomials related to rook theory and matchings in graphs. One of these families is based on the cover polynomial of a digraph introduced by Chung and Graham [ChGr]. Another involves a version of the \hit polynomial" of rook theory, but which applies to weighted matchings in (non-bipartite) graphs. For both of these families we prove a result which is anal...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3113