53 citations · 618 across the 64 of their papers we have counts for
25 papers · 1 filter
Signed Generalized Stirling Polynomials, Nested Sums, and Hyperbolic Secant Integral Identities
Abdulhafeez A. Abdulsalam, Michael J. Schlosser
We study signed generalized Stirling polynomials arising in closed forms for Malmsten-type hyperbolic secant integrals. Their product structure is used to prove recurren…
Expansions of averaged truncations of basic hypergeometric series
Michael J. Schlosser, Nian Hong Zhou
Motivated by recent work of George Andrews and Mircea Merca on the expansion of the quotient of the truncation of Euler's pentagonal number series by the complete series, we provid…
On an identity of Chaundy and Bullard. III. Basic and elliptic extensions
Natsuko Hoshi, Makoto Katori, Tom H. Koornwinder +1
The identity by Chaundy and Bullard expresses as a sum of two truncated binomial series in one variable where the truncations depend on two different non-negative integers. We…
A weighted extension of Fibonacci numbers
Gaurav Bhatnagar, Archna Kumari, Michael J. Schlosser
We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci identities. As a special case, we propose an elliptic extension which extends the -Fibonacci…
Lattice paths and negatively indexed weight-dependent binomial coefficients
Josef Küstner, Michael J. Schlosser, Meesue Yoo
In 1992, Loeb considered a natural extension of the binomial coefficients to negative entries and gave a combinatorial interpretation in terms of hybrid sets. He showed that many o…
Elliptic solutions of dynamical Lucas sequences
Michael J. Schlosser, Meesue Yoo
We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version i…
Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow
Hsien-Kuei Hwang, Emma Yu Jin, Michael J. Schlosser
We establish the asymptotic normality of the dimension of large-size random Fishburn matrices by a complex-analytic approach. The corresponding dual problem of size distribution un…
Proof of a bi-symmetric septuple equidistribution on ascent sequences
Emma Yu Jin, Michael J. Schlosser
It is well known since the seminal work by Bousquet-Mélou, Claesson, Dukes and Kitaev (2010) that certain refinements of the ascent sequences with respect to several natural statis…
Enumeration of standard barely set-valued tableaux of shifted shapes
Jang Soo Kim, Michael J. Schlosser, Meesue Yoo
A standard barely set-valued tableau of shape is a filling of the Young diagram with integers such that the integers are increasing in each row and column…
A tribute to Dick Askey
Michael J. Schlosser
This is a small contribution to the (September 15, 2019) Liber Amicorum Richard "Dick" Allen Askey. At the end a positivity conjecture related to the First and Second Borwein Conje…
A partial theta function Borwein conjecture
Gaurav Bhatnagar, Michael J. Schlosser
We present an infinite family of Borwein type conjectures. The expressions in the conjecture are related to multiple basic hypergeometric series with Macdonald polynomial…
Bilateral identities of the Rogers--Ramanujan type
Michael J. Schlosser
We derive by analytic means a number of bilateral identities of the Rogers--Ramanujan type. Our results include bilateral extensions of the Rogers--Ramanujan and the Göllnitz-Gordo…
Weight-dependent commutation relations and combinatorial identities
Michael J. Schlosser, Meesue Yoo
We derive combinatorial identities for variables satisfying specific systems of commutation relations, in particular elliptic commutation relations. The identities thus obtained ex…
Combinatorial interpretations of Ramanujan's tau function
Frank Garvan, Michael J. Schlosser
We use a q-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan's tau function which involves t-cores and a new class of partitions which we call (m,k)-…
Basic hypergeometric summations from rook theory
Michael J. Schlosser, Meesue Yoo
We employ a one-variable extension of q-rook theory to give combinatorial proofs of some basic hypergeometric summations, including the q-Pfaff-Saalschütz summation and a 4phi3 sum…
Elliptic extensions of the alpha-parameter model and the rook model for matchings
Michael J. Schlosser, Meesue Yoo
We construct elliptic extensions of the alpha-parameter rook model introduced by Goldman and Haglund and of the rook model for matchings of Haglund and Remmel. In particular, we ex…
An elliptic extension of the general product formula for augmented rook boards
Michael J. Schlosser, Meesue Yoo
Rook theory has been investigated by many people since its introduction by Kaplansky and Riordan in 1946. Goldman, Joichi and White in 1975 showed that the sum over of the prod…
Elliptic rook and file numbers
Michael J. Schlosser, Meesue Yoo
Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel's q-rook numbers by two add…
The major index generating function of standard Young tableaux of shapes of the form "staircase minus rectangle"
Christian Krattenthaler, Michael J. Schlosser
A specialisation of a transformation formula for multi-dimensional elliptic hypergeometric series is used to provide compact, non-determinantal formulae for the generating function…
Recurrence formulas for Macdonald polynomials of type A
Michel Lassalle, Michael J. Schlosser
We consider products of two Macdonald polynomials of type A, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero…
Macdonald Polynomials and Multivariable Basic Hypergeometric Series
Michael J. Schlosser
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…
Elliptic enumeration of nonintersecting lattice paths
Michael Schlosser
We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. T…
Inversion of the Pieri formula for Macdonald polynomials
Michel Lassalle, Michael Schlosser
We give the explicit analytic development of Macdonald polynomials in terms of "modified complete" and elementary symmetric functions. These expansions are obtained by inverting th…
An analytic formula for Macdonald polynomials
Michel Lassalle, Michael Schlosser
We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtai…