相关论文: A New Grounded Partition Identity of Type $D_4^{(3…

We find involutions for three Rogers-Ramanujan-Gordon type identities obtained by Andrews on the generating functions for partitions with part difference and parity restrictions.

Relations involving the Rogers-Ramanujan continued fractions $R(q),$ $R(q^3 ),$ and $R(q^4)$ are used to find new generating functions and congruences modulo 5 and 25 for 3-core, 4-core, 4-regular, and colored partition functions.

Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding…

We prove and conjecture some new symmetric function identities, which equate the generating series of 1. Plane partitions, subject to certain restrictions and weightings, and 2. Alternating sign matrices, subject to certain symmetry…

We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions to the famous Andrews-Gordon identities. Our tools involve…

In the first paper of this series, we gave infinite families of coloured partition identities which generalise Primc's and Capparelli's classical identities. In this second paper, we study the representation theoretic consequences of our…

We consider an identity relating Fibonacci numbers to Pascal's triangle discovered by G. E. Andrews. Several authors provided proofs of this identity, most of them rather involved or else relying on sophisticated number theoretical…

The partition statistic $V_R$-rank is introduced to give combinatorial proofs of the Ramanujan type congruences mod 3 for certain classes of partition functions.

We prove some new modular identities for the Rogers\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\textendash Ramanujan continued fraction, then…

We shall realize certain affine geometric crystal of type $D_4^{(3)}$ associated with the fundamental representation $W(\pi_1)$ explicitly . By its explicit form, we see that it has a positive structure.

In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called {\it partitions with designated summands}. These are built by taking unrestricted integer partitions and designating exactly one of each occurrence…

In this we paper we prove several new identities of the Rogers-Ramanujan-Slater type. These identities were found as the result of computer searches. The proofs involve a variety of techniques, including series-series identities, Bailey…

We study certain arithmetic properties of an analogue $B(n)$ of Lin's restricted partition function that counts the number of partition triples $\pi=(\pi_1,\pi_2,\pi_3)$ of $n$ such that $\pi_1$ and $\pi_2$ comprise distinct odd parts and…

The product sides of the Rogers--Ramanujan identities and alike often appear to be "transparently modular" (functions). The old work by Rogers (1894) and recent work by Rosengren make use (somewhat implicitly) of this fact for proving the…

Recently Amdeberhan, Sellers, and Singh introduced a new infinite family of partition functions called generalized cubic partitions. Given a positive integer $d$, they let $a_d(n)$ be the counting function for partitions of $n$ in which the…

We present what we call a "motivated proof" of the Bressoud-G\"ollnitz-Gordon partition identities. Similar "motivated proofs" have been given by Andrews and Baxter for the Rogers-Ramanujan identities and by Lepowsky and Zhu for Gordon's…

In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned…

The G\"ollnitz-Gordon-Andrews identities generalize the partition identities discovered independently by H. G\"ollnitz and B. Gordon. In this article, we present a commutative algebra proof of the G\"ollnitz-Gordon-Andrews identities. More…

We examine an identity originally stated in Ramanujan's ``lost notebook'' and first proven algebraically by Andrews and combinatorially by Kim. We give two independent combinatorial proofs and interpretations of this identity, which also…

We conjecture polynomial identities which imply Rogers--Ramanujan type identities for branching functions associated with the cosets $({\cal G}^{(1)})_{\ell-1}\otimes ({\cal G}^{(1)})_{1} / ({\cal G}^{(1)})_{\ell}$, with ${\cal…