20 citations · 135 across the 49 of their papers we have counts for
57 papers
Linked partition ideals and Russell's three-colored partitions
Shane Chern
Russell recently introduced a family of three-colored partitions in analogy with earlier work by Alladi and Gordon. He showed that their enumerations are surprisingly connected to…
Elementary Proofs of Arithmetic Properties for Schur-Type Overpartitions Modulo Small Powers of 2
Shane Chern, Robson da Silva, James A. Sellers
In 2022, Broudy and Lovejoy extensively studied the function which counts the number of overpartitions of \emph{Schur-type}. In particular, they proved a number of congruenc…
An infinite family of internal congruences modulo powers of 2 for partitions into odd parts with designated summands
Shane Chern, James A. Sellers
In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called \emph{partitions with designated summands}. These are built by taking unrestricted integ…
Hitting a prime by rolling a die with infinitely many faces
Shane Chern
Alon and Malinovsky recently proved that it takes on average rolls of fair six-sided dice until the first time the total sum of all rolls arrives at a prime. Natura…
Hankel determinants and Jacobi continued fractions for -Euler numbers
Shane Chern, Lin Jiu
The -analogs of Bernoulli and Euler numbers were introduced by Carlitz. Similar to the recent results on the Hankel determinants for the -Bernoulli numbers established by Cha…
Linked partition ideals and a family of quadruple summations
George E. Andrews, Shane Chern
Recently, -regular partitions into distinct parts are connected with a family of overpartitions. In this paper, we provide a uniform extension of two relations due to Andrews fo…