# New enumeration formulas for alternating sign matrices and square ice partition functions

@article{Ayyer2012NewEF, title={New enumeration formulas for alternating sign matrices and square ice partition functions}, author={Arvind Ayyer and Dan Romik}, journal={Advances in Mathematics}, year={2012}, volume={235}, pages={161-186} }

## 15 Citations

### The volume and ehrhart polynomial of the alternating sign matrix polytope

- Mathematics
- 2019

Alternating sign matrices (ASMs), polytopes and partially-ordered sets are fascinating combinatorial
objects which form the main themes of this thesis.
In Chapter 1, the origins and various aspects…

### A doubly-refined enumeration of alternating sign matrices and descending plane partitions

- MathematicsJ. Comb. Theory, Ser. A
- 2013

### Short proof of the ASM theorem avoiding the six-vertex model

- MathematicsJ. Comb. Theory, Ser. A
- 2016

### Diagonally and antidiagonally symmetric alternating sign matrices of odd order

- MathematicsDiscrete Mathematics & Theoretical Computer Science
- 2020

### ALTERNATING SIGN MATRIX ENUMERATION INVOLVING NUMBERS OF INVERSIONS AND -1's AND POSITIONS OF BOUNDARY 1's (Algebraic Combinatorics related to Young diagram and statistical physics)

- Mathematics
- 2014

This paper consists of a review of results for the exact enumeration of alternating sign matrices of fixed size with prescribed values of some or all of the following six statistics: the numbers of…

### Refined enumeration of symmetry classes of alternating sign matrices

- MathematicsJ. Comb. Theory, Ser. A
- 2021

### Inversions and the Gog-Magog problem

- Mathematics
- 2014

We consider the problem of finding a bijection between the sets of alternating sign matrices and of totally symmetric self complementary plane partitions, which can be reformulated using Gog and…

### Quantum integrable combinatorics of Schur polynomials

- Mathematics
- 2015

We examine and present new combinatorics for the Schur polynomials from the viewpoint of quantum integrability. We introduce and analyze an integrable six-vertex model which can be viewed as a…

## References

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- 2012

### A doubly-refined enumeration of alternating sign matrices and descending plane partitions

- MathematicsJ. Comb. Theory, Ser. A
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- MathematicsJ. Comb. Theory, Ser. A
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### Refined enumerations of alternating sign matrices: monotone (d,m)-trapezoids with prescribed top and bottom row

- Mathematics
- 2009

Monotone triangles are plane integer arrays of triangular shape with certain monotonicity conditions along rows and diagonals. Their significance is mainly due to the fact that they correspond to n×n…

### Izergin-Korepin Determinant at a Third Root of Unity

- Mathematics
- 2006

We consider the partition function of the inhomogeneous six-vertex model defined on an n×n square lattice. This function depends on 2n spectral parameters xi and yi attached to the respective…

### Proof of the Razumov-Stroganov conjecture

- Mathematics
- 2006

We define link patterns in a combinatorial way, and construct an action of the extended affine Temperley-Lieb algebra with weight 1 on the complex vectorspace with the link patterns as basis, using a…

### Alternating-Sign Matrices and Domino Tilings (Part I)

- Mathematics
- 1992

We introduce a family of planar regions, called Aztec diamonds, and study tilings of these regions by dominoes. Our main result is that the Aztec diamond of order n has exactly 2n(n+1)/2 domino…