28 citations · 147 across the 20 of their papers we have counts for
7 papers · 1 filter
The product of parts or "norm" of a partition
Andrew V. Sills, Robert Schneider
In this article we study the "norm" of an integer partition, which we define to be the product of the parts. This partition-theoretic statistic has appeared here and there in the l…
Finite Rogers--Ramanujan type identities
Andrew V. Sills
Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of…
Rogers-Ramanujan-Slater Type Identities
James Mc Laughlin, Andrew V. Sills, Peter Zimmer
In this survey article, we present an expanded version of Lucy Slater's famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were dis…
On a pair of identities from Ramanujan's lost notebook
James Mc Laughlin, Andrew V. Sills
Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immedia…
Hybrid Proofs of the -Binomial Theorem and other identities
Dennis Eichhorn, James Mc Laughlin, Andrew V. Sills
We give "hybrid" proofs of the -binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the…
Polynomial Generalizations of two-variable Ramanujan type identities
James Mc Laughlin, Andrew V. Sills
We provide finite analogs of a pair of two-variable -series identities from Ramanujan's lost notebook and a companion identity.