相关论文: On refined enumerations of some symmetry classes o…
The refined enumeration of alternating sign matrices (ASMs) of given order having prescribed behavior near one or more of their boundary edges has been the subject of extensive study, starting with the Refined Alternating Sign Matrix…
We prove refined enumeration results on several symmetry classes as well as related classes of alternating sign matrices with respect to classical boundary statistics, using the six-vertex model of statistical physics. More precisely, we…
Alternating sign matrices with a U-turn boundary (UASMs) are a recent generalization of ordinary alternating sign matrices. Here we show that variations of these matrices are in bijective correspondence with certain symplectic shifted…
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…
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 study a further refinement of the standard refined enumeration of alternating sign matrices (ASMs) according to their first two rows instead of just the first row, and more general "d-refined" enumerations of ASMs according to the first…
In 2007, the first author gave an alternative proof of the refined alternating sign matrix theorem by introducing a linear equation system that determines the refined ASM numbers uniquely. Computer experiments suggest that the numbers…
It was shown by Kuperberg that the partition function of the square-ice model related to the quarter-turn symmetric alternating-sign matrices of even order is the product of two similar factors. We propose a square-ice model whose states…
We prove the equality of doubly refined enumerations of Alternating Sign Matrices and of Totally Symmetric Self-Complementary Plane Partitions using integral formulae originating from certain solutions of the quantum Knizhnik--Zamolodchikov…
The aim of this work is to enumerate alternating sign matrices (ASM) that are quasi-invariant under a quarter-turn. The enumeration formula (conjectured by Duchon) involves, as a product of three terms, the number of unrestricted ASM's and…
The aim of this work is to enumerate alternating sign matrices (ASM) that are quasi-invariant under a quarter-turn. The enumeration formula (conjectured by Duchon) involves, as a product of three terms, the number of unrestricted ASM's and…
The six-vertex model with Domain Wall Boundary Conditions, or square ice, is considered for particular values of its parameters, corresponding to 1-, 2-, and 3-enumerations of Alternating Sign Matrices (ASMs). Using Hankel determinant…
In recent papers we have studied refined enumerations of alternating sign matrices with respect to a fixed set of top and bottom rows. The present paper is a first step towards extending these considerations to alternating sign matrices…
I consider the partition function of the inhomogeneous 6-vertex model defined on the $n$ by $n$ square lattice. This function depends on 2n spectral parameters $x_i$ and $y_i$ attached to the horizontal and vertical lines respectively. In…
It was shown by Kuperberg that the partition function of the square-ice model related to half-turn symmetric alternating-sign matrices of even order is the product of two similar factors. We propose a square-ice model whose states are in…
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…
This paper is the second in a series of planned papers which provide first bijective proofs of alternating sign matrix results. Based on the main result from the first paper, we construct a bijective proof of the enumeration formula for…
We study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order by introducing a case of the six-vertex model whose configurations are in bijection with such matrices. The model…
An Alternating Sign Matrix (ASM) is a square matrix with entries in $\{0,1,-1\}$, and such that: $i)$ in each row and columns, nonzero entries alternate in sign; $ii)$ for any given row or column, entries sum up to 1. We define the…
Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result using an analysis of the six-vertex state model (also called…