Related papers: Lattice models and generalized Rogers Ramanujan id…
For any rational number $p_0\ge 1$ we prove an identity of Rogers-Ramanujan-Gordon-Andrews' type. Bijection between the space of states for XXZ model and that of XXX model is constructed.
We derive by analytic means a number of bilateral identities of the Rogers--Ramanujan type. Our results include bilateral extensions of the Rogers--Ramanujan and the G\"ollnitz-Gordon identities, and of related identities by Ramanujan,…
We examine a method to conjecture two very famous identities that were conjectured by Ramanujan, and later found to be known to Rogers.
J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In a joint work with Arne Meurman this approach is…
We establish some new bilateral double-sum Rogers-Ramanujan identities involving parameters. As applications, these identities yield several new multi-sum Rogers-Ramanujan type identities. Our proofs utilize the theory of basic…
We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schr\"odinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment…
Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for $\hat{\goth{sl}(2)}$ satisfy certain classical recursion formulas…
We prove seven of the Rogers-Ramanujan type identities modulo $12$ that were conjectured by Kanade and Russell. Included among these seven are the two original modulo $12$ identities, in which the products have asymmetric congruence…
In the first three papers, we conducted a series of discussions on the statistics of strict partitions and Rogers-Ramanujan partitions, specifically the sequences of odd length (denoted as $\mathrm{sol}$) and its extensions. We established…
Many classical $q$-series identities, such as the Rogers--Ramanujan identities, yield combinatorial interpretations in terms of integer partitions. Here we consider algebraically manipulating some of the classical $q$-series to yield…
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 immediately implies an infinite family of Rogers-Ramanujan type…
We give simple elementary proofs of Bressoud's and Schur's polynomial versions of the Rogers-Ramanujan identities
Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local…
Recently, Rosengren utilized an integral method to prove a number of conjectural identities found by Kanade and Russell. Using this integral method, we give new proofs to some double sum identities of Rogers-Ramanujan type. These identities…
Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers-Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical physics. One of these areas is…
A few years ago Foda, Quano, Kirillov and Warnaar proposed and proved various finite analogs of the celebrated Andrews-Gordon identities. In this paper we use these polynomial identities along with the combinatorial techniques introduced in…
We describe the story of the Rogers-Ramanujan identities; being known for 85 years and having about 130 pure mathematics proofs, suddenly entering physics when Rodney Baxter solved the Hard Hexagon Model in Statistical Mechanics in 1980. We…
The Rogers-Ramanujan-Gordon identities generalize the classical partition identities discovered independently by L. J. Rogers and S. Ramanujan. In 2021, Afsharijoo provided a commutative algebra proof of the Rogers-Ramanujan-Gordon…
Ramanujan listed several q-series identities in his lost notebook. The most well known q-series identities are the Rogers-Ramanujan type identities which are first discovered by Rogers and then rediscovered by Ramanujan. In this paper, we…
The theory of Bailey's transform provides a systematic method for deriving $q$-identities, the key factor of which is the Bailey pair. The concept of Bailey pair was first extended to bilateral version by Paule. In this paper, following…