相关论文: A remark on certain restricted plane partitions an…
We give a product formula for the number of shifted plane partitions of shifted double staircase shape with bounded entries. This is the first new example of a family of shapes with a plane partition product formula in many years. The proof…
A new recursive procedure for calculation of restricted partition function is suggested. An explicit formula for the restricted partition function is found based on this procedure.
In this letter we calculate the exact partition function for free bosons on the plane with lacunae. First the partition function for a plane with two spherical holes is calculated by matching exactly for the infinite set of Wilson…
This paper explores integrable structures of a generalized melting crystal model that has two $q$-parameters $q_1,q_2$. This model, like the ordinary one with a single $q$-parameter, is formulated as a model of random plane partitions (or,…
We calculate the partition functions of the affine Pasquier models on the cylinder in the continuum limit. We show that the partition function of any affine model may be expressed in terms of the orbit structure of the affine Coxeter…
We give a Pfaffian formula to compute the partition function of the Ising model on any graph $G$ embedded in a closed, possibly non-orientable surface. This formula, which is suitable for computational purposes, is based on the relation…
Inspired by Gansner's elegant $k$-trace generating function for rectangular plane partitions, we introduce two novel operators, $\varphi_{z}$ and $\psi_{z}$, along with their combinatorial interpretations. Through these operators, we derive…
We perform the calculation of the partition function of the Poisson-sigma model on the world sheet with the topology of a two-dimensional disc. Considering the special case of a linear Poisson structure we recover the partition function of…
A close connection of reverse plane partitions with an integrable dynamical system called the discrete two-dimensional (2D) Toda molecule is clarified. It is shown that a multiplicative partition function for reverse plane partition of…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
Stanley generalized MacMahon's classical theorem by proving a product formula for the norm-trace generating function for plane partition with unbounded parts. In his recent work on biothorgonal polynomials, Kamioka proved a finite analogue…
In this paper, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our…
The number of plane partitions contained in a given box was shown by MacMahon to be given by a simple product formula. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths $a,b,c,a,b,c$ (in cyclic…
We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric examples. They can be written as products of (generalized)…
We outline a method of calculation of partition functions of orientable manifolds with fluctuating metric and perform the calculation for the specific case of the unit interval.
Motivated by string theory connection, a covariant procedure for perturbative calculation of the partition function of the two-dimensional generalized $\sigma$-model is considered. The importance of a consistent regularization of the…
We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a…
This is a review of the authors' recent results on an integrable structure of the melting crystal model with external potentials. The partition function of this model is a sum over all plane partitions (3D Young diagrams). By the method of…
Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix…
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…