28 citations · 148 across the 22 of their papers we have counts for
11 papers · 2 filters
Combinatorics of Ramanujan--Slater type identities
James Mc Laughlin, Andrew V. Sills
We provide the missing member of a family of four -series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinato…
On the ordinary and signed Göllnitz--Gordon partitions
Andrew V. Sills
Dedicated to George E. Andrews on the occasion of his 70th birthday. Submitted to a special issue for this occasion. We use Andrews' notion of a `signed partition' (i.e. partition…
Disturbing the -Dyson Conjecture
Andrew V. Sills
I discuss the computational methods behind the formulation of some conjectures related to variants on Andrews' -Dyson conjecture.
Disturbing the Dyson conjecture in a \emph{generally} GOOD way
Andrew V. Sills
Dyson's celebrated constant term conjecture ({\em J. Math. Phys.}, 3 (1962): 140--156) states that the constant term in the expansion of $\prod_{1\leqq i\neq j\leqq n} (1-x_i/x_j)^…
The combinatorics of MacMahon's partial fractions
Andrew V. Sills
MacMahon showed that the generating function for partitions into at most parts can be decomposed into a partial fractions-type sum indexed by the partitions of . In this pre…
Disturbing the Dyson Conjecture (in a GOOD Way)
Andrew V. Sills, Doron Zeilberger
We present a case study in {\it experimental} yet {\it rigorous} mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that {\it automatically co…