Independence polynomials and hypergeometric series
نویسندگان
چکیده
Let Γ be a simple graph and I ( x ) its multivariate independence polynomial. The main result of this paper is the characterization chordal graphs as only for which power series expansion − 1 Horn hypergeometric.
منابع مشابه
Macdonald Polynomials and Multivariable Basic Hypergeometric Series
Abstract. We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised 6φ5 summation formula. We derive several new related identities including ...
متن کاملBisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series
A new type of sl3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl3 basic hypergeometric series is a bisymmetric function related to Macdonald’s commuting family of q-difference operators, to the sl3 Selberg integrals of Tarasov and Varchenko, and to alternati...
متن کاملNONSYMMETRIC INTERPOLATION MACDONALD POLYNOMIALS AND gln BASIC HYPERGEOMETRIC SERIES
The Knop–Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gln. Our main results include a new q-binomial theorem, new q-Gauss sum, and several transformation formulae for gln series.
متن کاملHypergeometric Polynomials and Integer Programming
We examine connections between A-hypergeometric di erential equations and the theory of integer programming. In the rst part, we develop a \hypergeometric sensitivity analysis" for small variations of constraint constants with creation operators and b-functions. In the second part, we study the indicial polynomial (b-function) along the hyperplane x i = 0 via a correspondence between the optima...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of The London Mathematical Society
سال: 2021
ISSN: ['1469-2120', '0024-6093']
DOI: https://doi.org/10.1112/blms.12545