Related papers: A vector partition function for the multiplicities…

A new type of sl_3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl_3 basic hypergeometric series is a…

In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The marked-graph bracket polynomial is readily…

The complexity of graph homomorphisms has been a subject of intense study [11, 12, 4, 42, 21, 17, 6, 20]. The partition function $Z_{\mathbf A}(\cdot)$ of graph homomorphism is defined by a symmetric matrix $\mathbf A$ over $\mathbb C$. We…

Fully inhomogeneous spin Hall-Littlewood symmetric rational functions $F_\lambda$ are multiparameter deformations of the classical Hall-Littlewood symmetric polynomials and can be viewed as partition functions in $\mathfrak{sl}(2)$ higher…

We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses…

We introduce a class of Hermitian metrics, that we call pluriclosed star split, generalising both the astheno-K\"ahler metrics of Jost and Yau and the $(n-2)$-Gauduchon metrics of Fu-Wang-Wu on complex manifolds. They have links with…

We introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the $U_q(sl_2)$…

Through dualities on representations on tensor powers and symmetric powers respectively, the partition algebra and multiset partition algebra have been used to study long-standing questions in the representation theory of the symmetric…

The section volume function $A_K(\xi,t), \ \xi \in \mathbb R^n, \ t \in \mathbb R,$ of a body $K \subset \mathbb R^n$ evaluates the $(n-1)$-dimensional volume of the cross-section $K$ by the hyperplane $\{ x \cdot \xi=t \}.$ We are…

We study symplectic forms on hypersurface algebroids. These are a broad generalization of the $b^{k}$-Poisson structures studied extensively by Miranda, Scott, and collaborators, and their geometry is intimately related to the group of…

Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and…

A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex $u\in V$ a weight that equals the corresponding…

This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators $\{ T_m: \, m \ge 1\}$ given by $T_m(f)(a, c) = \frac{1}{m} \sum_{k=0}^{m-1} f(\frac{a+k}{m},…

The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces of an abelian automorphism subgroup is shown to act as the adjacency matrix of a weighted subspace lattice. The connection between the latter and…

From our work on partition functions in log gravity, we show that the palindromic numerators in two variables of bigraded symmetric orbifold Hilbert series take the form of sums of products of Kostka-Foulkes polynomials associated with a…

Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well understood, the number of terms considered in Kostant's formula…

Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class…

This paper gives an exposition of well known results on vector partition functions. The exposition is based on works of M. Brion, A. Szenes and M. Vergne and is geared toward explicit computer realizations. In particular, the paper presents…

We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power…

For motives associated with Fermat curves, there are elements in motivic cohomology whose regulators are written in terms of special values of generalized hypergeometric functions. Using them, we verify the Beilinson conjecture numerically…