相关论文: Generating functions for ranks of pre-modular cate…

Understanding the relationship between mock modular forms and quantum modular forms is a problem of current interest. Both mock and quantum modular forms exhibit modular-like transformation properties under suitable subgroups of…

In this note, we give a rank function axiomatization for delta-matroids and study the corresponding rank generating function. We relate an evaluation of the rank generating function to the number of independent sets of the delta-matroid,…

We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup.…

We classify module categories over the category of representations of quantum $SL(2)$ in a case when $q$ is not a root of unity. In a case when $q$ is a root of unity we classify module categories over the semisimple subquotient of the same…

We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally…

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…

In a seminal 2007 paper, Andrews introduced a class of combinatorial objects that generalize partitions called $k$-marked Durfee symbols. Multivariate rank generating functions for these objects have been shown by many to have interesting…

We introduce the notion of a rank function on a triangulated category $\mathcal{C}$ which generalizes the Sylvester rank function in the case when $\mathcal{C}=\operatorname{Perf}(A)$ is the perfect derived category of a ring $A$. We show…

We define a generalized vector partition function and derive an identity for generating series of such functions associated with solutions of basic recurrence relation of combinatorial analysis. As a consequence, we obtain the generating…

In this paper a Kummer theory of division points over rank one Drinfeld A=Fq[T]-modules defined over global function fields was given. The results are in complete analogy with the classical Kummer theory of division points over the…

We derive the P-finite recurrences for classes of sequences with ordinary generating function containing roots of polynomials. The focus is on establishing the D-finite differential equations such that the familiar steps of reducing their…

In this paper we construct the quantum group, at roots of unity, of abelian Chern-Simons theory. We then use it to model classical theta functions and the actions of the Heisenberg and modular groups on them.

We connect a primitive operation from arithmetic -- summing the digits of a base-$B$ integer -- to $q$-series and product generating functions analogous to those in partition theory. We find digit sum generating functions to be intertwined…

We describe all Gaussian generating functionals on several easy quantum groups given by non-crossing partitions. This includes in particular the free unitary, orthogonal and symplectic quantum groups. We further characterize central…

In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…

We consider the classification problem for rank 4 premodular categories. We uncover a formula for the 2nd Frobenius-Schur indicator of a premodular category, and complete the classification of rank 4 premodular categories (up to…

In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulas for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulas for the…

Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital $*$-subalgebra with core-like properties in its domain. On the other hand we prove that every…

We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…