Related papers: 2-colored Rogers-Ramanujan partition identities

We show that any complete $k$-partite graph $G$ on $n$ vertices, with $k \ge 3$, whose edges are two-coloured, can be covered with two vertex-disjoint monochromatic paths of distinct colours. We prove this under the necessary assumption…

Kaur, Rana, and Eyyunni recently defined the mex sequence of a partition and established, by analytic methods, connections to two disparate types of partition-related objects. We make a bijection between partitions with certain mex…

Partitions with initial repetitions were introduced by George Andrews. We consider a subclass of these partitions and find Legendre theorems associated with their respective partition functions. The results in turn provide partition…

This paper is concerned with a class of partition functions $a(n)$ introduced by Radu and defined in terms of eta-quotients. By utilizing the transformation laws of Newman, Schoeneberg and Robins, and Radu's algorithms, we present an…

Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.

Pattern avoidance in the symmetric group $S_n$ has provided a number of useful connections between seemingly unrelated problems from stack-sorting to Schubert varieties. Recent work has generalized these results to $S_n\wr C_c$, the objects…

We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…

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 generalization that encapsulates both families. These were discovered…

We show that for any $2$-local colouring of the edges of the balanced complete bipartite graph $K_{n,n}$, its vertices can be covered with at most~$3$ disjoint monochromatic paths. And, we can cover almost all vertices of any complete or…

We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').

Within the framework of unitary easy quantum groups, we study an analogue of Brauer's Schur-Weyl approach to the representation theory of the orthogonal group. We consider concrete combinatorial categories whose morphisms are formed by…

Recently, Pankaj Jyoti Mahanta and Manjil P. Saikika proved some identities relating certain restricted partitions into distinct odd parts with the partition whose odd parts are distinct combinatorially. They asked for the q-series proofs.…

In a 2016 paper, Straub proved an analogue to Euler's partition identity for partitions with fixed perimeter. Later, Fu and Tang provided a refinement and generalization of Straub's analogue to $d$-distinct partitions as well as a result…

In this short note, we give basic enumerative results on colored integer partitions.

In 2003, Alladi, Andrews and Berkovich proved an identity for partitions where parts occur in eleven colors: four primary colors, six secondary colors, and one quaternary color. Their work answered a longstanding question of how to go…

Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…

We present two new Ramanujan-type congruences modulo 5 for overpartition. We also give an affirmative answer to a conjecture of Dou and Lin, which includes four congruences modulo 25 for overpartition.

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 discovered after the publication of Slater's papers, and older…

We give a new proof of Chan's identity involving the cubic partition function and we also give a new identity for the cubic partition function which is analogues to the Zuckerman's identity for the ordinary partition function.

In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the…