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math.NT2025
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.
math.CO2025
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…
math.NT2025
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.