7 papers
A local bijection between alternating sign matrices and descending plane partitions and a Striker--Fulmek-type -statistic
Michael J. Schlosser
We prove a local bijection between alternating sign matrices (ASMs) and descending plane partitions (DPPs) in the refined fibres of Behrend--Di Francesco--Zinn-Justin. The map is c…
Bilateral -ultraspherical functions
Michael J. Schlosser
We introduce the bilateral -ultraspherical functions, a bilateral-series extension of the continuous -ultraspherical polynomials. They are defined by specific bilateral basic…
Product formulas for basic hypergeometric series by evaluations of Askey--Wilson polynomials
Howard Cohl, Michael Schlosser
Ismail and Wilson derived a generating function for Askey--Wilson polynomials which is given by a product of -Gauss (Heine) nonterminating basic hypergeometric functions. We pro…
Transformations and summations for bilateral basic hypergeometric series
Howard S. Cohl, Michael J. Schlosser
We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two impor…
Diagonal operators, -Whittaker functions and rook theory
Samrith Ram, Michael J. Schlosser
We discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finit…
A family of orthogonal functions on the unit circle and a new multilateral matrix inverse
Michael J. Schlosser
Using Bailey's very-well-poised summation, we show that a specific sequence of well-poised bilateral basic hypergeometric series form a family of orthogonal funct…