7 papers
More minor summation formulae
Shane Chern, Theresia Eisenkölbl, Ilse Fischer +8
We prove determinantal-Pfaffian formulae that simultaneously generalise the Pfaffian minor summation formula of Ishikawa and Wakayama and Byun's recent minor summation formula. The…
Asymptotics for the Enumeration of Commuting Matrices over Finite Fields
Kathrin Bringmann, Shane Chern, Johann Franke +1
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
Domino tilings, nonintersecting lattice paths and subclasses of Koutschan-Krattenthaler-Schlosser determinants
Qipin Chen, Shane Chern, Atsuro Yoshida
Koutschan, Krattenthaler and Schlosser recently considered a family of binomial determinants. In this work, we give combinatorial interpretations of two subclasses of these determi…
A probabilistic proof of Euler's pentagonal number theorem
Shane Chern
We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.
Multiple Rogers--Ramanujan type identities for torus links
Shane Chern
In this paper, we establish simple -fold summation expressions for the Quot and motivic Cohen--Lenstra zeta functions associated with the torus links. Such expressions…
Juhl type formulas for curved Ovsienko--Redou operators
Shane Chern, Zetian Yan
We prove Juhl type formulas for the curved Ovsienko--Redou operators and their linear analogues, which indicate the associated formal self-adjointness, thereby confirming two conje…
On the -measure of partitions and distinct partitions
George E. Andrews, Shane Chern, Zhitai Li
The -measure of an integer partition was recently introduced by Andrews, Bhattacharjee and Dastidar. In this paper, we establish trivariate generating function identities counti…