相关论文: Enumerations of half-turn symmetric alternating-si…

We introduce a new family $\mathcal{A}_{n,k}$ of Schur positive symmetric functions, which are defined as sums over totally symmetric plane partitions. In the first part, we show that, for $k=1$, this family is equal to a multivariate…

Recently, Hirschhorn and Sellers defined the partition function $a_r(n)$, which counts the number of partitions of $n$ wherein even parts come in only one color, while the odd parts may appear in one of $r$-colors for fixed $r\ge1$. The aim…

The appearance of numbers enumerating alternating sign matrices in stationary states of certain stochastic processes is reviewed. New conjectures concerning nest distribution functions are presented as well as a bijection between certain…

Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers-Ramanujan identities, the Gollnitz-Gordon identities, Euler's odd=distinct theorem, and the Andrews-Gordon…

We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set…

We investigate analogues of alternating sign matrices, called partial alternating sign matrices. We prove bijections between these matrices and several other combinatorial objects. We use an analogue of Wieland's gyration on fully-packed…

Four natural boundary statistics and two natural bulk statistics are considered for alternating sign matrices (ASMs). Specifically, these statistics are the positions of the 1's in the first and last rows and columns of an ASM, and the…

We solve the sign problem in a particle-hole symmetric spin-polarized fermion model on bipartite lattices using the idea of fermion bags. The solution can be extended to a class of models at half filling but without particle-hole symmetry.…

For each $\alpha \in \{0,1,-1 \}$, we count diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order with a maximal number of $\alpha$'s along the diagonal and the antidiagonal, as well as DASASMs of…

Since the alternating sign matrix conjecture, proposed by Mills, Robbins, and Rumsey in 1982, was proved by Zeilberger and Kuperberg, several refined enumerations have been considered. In particular, Behrend et al. obtained a quadruply…

The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function…

Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We put ASMs into a larger context by studying the order ideals of subposets of a…

We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The…

Motivated by the observation of partial magnetic order in kagome-based magnets, we study the classical kagome Ising antiferromagnet, known as kagome spin ice, including further-neighbor interactions at zero and finite temperature. While the…

In this note, we provide three new, very short proofs of two interesting congruences for Merca's partition function $a(n)$, which enumerates integer partitions where the odd parts have multiplicity at most 2. These modulo 2 congruences were…

We develop a novel quantum transfer matrix method to study thermodynamic properties of one-dimensional (1D) disordered electronic systems. It is shown that the partition function can be expressed as a product of $2\times2$ local transfer…

The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…

e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine…

In a previous article [math.CO/9712207], we derived the alternating-sign matrix (ASM) theorem from the Izergin-Korepin determinant for a partition function for square ice with domain wall boundary. Here we show that the same argument…

We use Schwinger's proper time method to compute the parity odd contributions to the U(1) current and energy-momentum tensor of an ideal gas of fermions in 2+1 dimensions in the presence of static gauge and gravitational backgrounds. From…