arXiv subjects
Publications and source records attributed to Pooneh Afsharijoo.
In this paper, we establish a new companion to the Göllnitz--Gordon identities. We give two independent proofs. The first is based on a new system of recurrence formulas, while the second uses generating series and the analytic form of the Göllnitz--Gordon identities.
We prove a family of partition identities involving integer partitions in three colors. The conditions imposed on the types of partitions appearing in these identities involve constraints that arise in the Rogers-Ramanujan and Andrews-Gordon identities, as well as in their recent extensions. The identities established in this paper are associated with the $A_r$ surface singularities via the arc HP-series, which provides a measure of singularities of algebraic varieties defined using arc spaces.
We prove a family of partition identities which is "dual" to the family of Andrews-Gordon's identities. These identities are inspired by a correspondence between a special type of partitions and "hypergraphs" and their proof uses combinatorial commutative algebra.
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 graded quotient rings, Durfee squares and rectangles for integer partitions, and $q$-series identities.
We give a commutative algebra viewpoint on Andrews recursive formula for the partitions appearing in "Gordon's identities", which are a generalization of Rogers-Ramanujan identities. Using this approach and differential ideals we conjecture a family of partition identities which extend Gordon's identities. This family is indexed by r >=2. We prove the conjecture for r=2 and r=3.
We prove a theorem which add a new member to Rogers-Ramanujan identities. This new member counts partitions with different type of constraints on even and odd parts. Generalizing this theorem, we obtain two family of partition identities of Rogers-Ramanujan type.
In the first part of this article, we consider a Groebner basis of the differential ideal {x_1^2} with respect to "the" weighted lexicographical monomial order and show that its computation is related with an identity involving the partitions that appear in the first Rogers-Ramanujan identity. We then prove that a Grobener basis of this ideal is not differentially finite in contrary with the case of "the" weighted reverse lexicographical order. In the second part, we give a simple and direct proof of a theorem of Nguyen Duc Tam about the Groaner basis of the differential ideal {x_1y_1}; we then obtain identities involving partitions with 2 colors.