Rook-by-rook rook theory: Bijective proofs of rook and hit equivalences
نویسندگان
چکیده
منابع مشابه
Rook Theory and Hypergeometric Series
The number of ways of placing k non-attacking rooks on a Ferrers board is expressed as a hypergeometric series, of a type originally studied by Karlsson and Minton. Known transformation identities for series of this type translate into new theorems about rook polynomials.
متن کاملRook Theory and t-Cores
If t is a positive integer, then a partition of a non-negative integer n is a t−core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of t. These partitions arise in the representation theory of finite groups and also in the theory of class numbers. We prove that if t = 2, 3, or 4, then two different t−cores are rook equivalent if and only if they are conjugates...
متن کاملRook Theory, Compositions, and Zeta Functions
A new family of Dirichlet series having interesting combinatorial properties is introduced. Although they have no functional equation or Euler product, under the Riemann Hypothesis it is shown that these functions have no zeros in Re(s) > 1/2. Some identities in the ring of formal power series involving rook theory and continued fractions are developed.
متن کاملm-Level rook placements
Goldman, Joichi, and White proved a beautiful theorem showing that the falling factorial generating function for the rook numbers of a Ferrers board factors over the integers. Briggs and Remmel studied an analogue of rook placements where rows are replaced by sets of m rows called levels. They proved a version of the factorization theorem in that setting, but only for certain Ferrers boards. We...
متن کاملGeneralized 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...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2009
ISSN: 0196-8858
DOI: 10.1016/j.aam.2008.09.003