5 papers
New central -binomial identities
Shane Chern, Karl Dilcher, Lin Jiu
We establish several new series evaluations involving the central -binomial coefficients, with the inspiration coming from earlier work by Vignat and one of the authors on the l…
Multi-headed lattices and Green functions
Qipin Chen, Shane Chern, Lin Jiu
Lattice geometries and random walks on them are of great interest for their applications in different fields such as physics, chemistry, and computer science. In this work, we focu…
q-Identities for parafermion theories
Peter Bouwknegt, Shane Chern, Bolin Han
In this paper we will prove a series of -identities suggested by the realisation of certain conformal field theories by so-called `coupled free fermions'. We will consider -s…
Leading coefficient in the Hankel determinants related to binomial and -binomial transforms
Shane Chern, Lin Jiu, Shuhan Li +1
It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to…
A central limit theorem for a card shuffling problem
Shane Chern, Lin Jiu, Italo Simonelli
Given a positive integer , consider a random permutation of the set . In , we look for sequences of consecutive integers that appear in adjacent positi…