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 کاملMultiple Hypergeometric Series – Appell Series and Beyond
This survey article (which will appear as a chapter in the book “Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions”, Springer-Verlag) provides a small collection of basic material on multiple hypergeometric series of Appell-type and of more general series of related type.
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 کاملGaussian Hypergeometric series and supercongruences
Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number of Fp points on algebraic varieties and to Fourier coefficients of modular forms. In this paper, we explicitly determine these functions modulo higher powers of p and discuss an application to super...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1996
ISSN: 0196-8858
DOI: 10.1006/aama.1996.0017