11 citations · 27 across the 14 of their papers we have counts for
16 papers
On a pair of three-colored (mod 10) partition identities
Matthew C. Russell
We prove a pair of (mod 10) partition identities. The sum sides involve three-colored partitions into distinct parts, while the product sides are the generating functions for disti…
Tight cylindric partitions
Shashank Kanade, Matthew C. Russell
In this note, we initiate the study of generating functions for tight cylindric partitions. For general (i.e., -rowed for ) tight cylindric partitions, we provide analo…
Remarks on the conjectures of Capparelli, Meurman, Primc and Primc
Shashank Kanade, Matthew C. Russell, Shunsuke Tsuchioka +1
In a series of two papers, S. Capparelli, A. Meurman, A. Primc, M. Primc (CMPP) and then M. Primc put forth three remarkable sets of conjectures, stating that the generating functi…
A refinement of and a companion to MacMahon's partition identity
Matthew C. Russell
We provide a refinement of MacMahon's partition identity on sequence-avoiding partitions, and use it to produce another mod 6 partition identity. In addition, we show that our tech…
Companions to the Andrews-Gordon and Andrews-Bressoud Identities and Recent Conjectures of Capparelli, Meurman, Primc, and Primc
Matthew C. Russell
We find bivariate generating functions for the cases of recently conjectured colored partition identities of Capparelli, Meurman, A. Primc, and M. Primc that are slight varia…
Principal subspaces of basic modules for twisted affine Lie algebras, -series multisums, and Nandi's identities
Katherine Baker, Shashank Kanade, Matthew C. Russell +1
We provide an observation relating several known and conjectured -series identities to the theory of principal subspaces of basic modules for twisted affine Lie algebras. We als…
Completing the Andrews-Schilling-Warnaar identities
Shashank Kanade, Matthew C. Russell
We study the Andrews-Schilling-Warnaar sum-sides for the principal characters of standard (i.e., integrable, highest weight) modules of . These characters have…
On certain identities involving Nahm-type sums with double poles
Shashank Kanade, Antun Milas, Matthew C. Russell
We prove certain Nahm-type sum representations for the (odd modulus) Andrews-Gordon identities, the (even modulus) Andrews-Bressoud identities, and Rogers' false theta functions. T…
On -series for principal characters of standard -modules
Shashank Kanade, Matthew C. Russell
We present sum-sides for principal characters of all standard (i.e., integrable and highest-weight) irreducible modules for the affine Lie algebra . We use modifications…
A variant of and some new identities of Rogers-Ramanujan-MacMahon type
Shashank Kanade, Debajyoti Nandi, Matthew C. Russell
We report on findings of a variant of - a Maple program that was used by two of the authors to conjecture several new identities of Rogers-Ramanujan kin…
Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
Shashank Kanade, Matthew C. Russell
We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture…
On a dual and an overpartition generalization of a family of identities of Andrews
Shashank Kanade, Matthew C. Russell
We present a dual of a family of partition identities of Andrews involving partitions with no repeated odd parts (among other conditions), along with an overpartition generalizatio…
IdentityFinder and some new identities of Rogers-Ramanujan type
Shashank Kanade, Matthew C. Russell
The Rogers-Ramanujan identities and various analogous identities (Gordon, Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities concerned with integer partition…
Ghost series and a motivated proof of the Andrews-Bressoud identities
Shashank Kanade, James Lepowsky, Matthew C. Russell +1
We present what we call a "motivated proof" of the Andrews-Bressoud partition identities for even moduli. A "motivated proof" of the Rogers-Ramanujan identities was given by G. E.…
A motivated proof of the Göllnitz-Gordon-Andrews identities
Bud Coulson, Shashank Kanade, James Lepowsky +4
We present what we call a "motivated proof" of the Göllnitz-Gordon-Andrews identities. A similar motivated proof of the Rogers-Ramanujan identities was previously given by G. E. An…
Noncommutative recursions and the Laurent phenomenon
Matthew C. Russell
We exhibit a family of sequences of noncommutative variables, recursively defined using monic palindromic polynomials in , and show that each possesses the Laurent ph…