A new determinant for the Q-enumeration of alternating sign matrices

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

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 Conjecture of Mills-Robbins-Rumsey [25], its proof by Zeilberger [31], and more recent work on doublyrefined and triply-refined enumeration by several authors. In ...

A formula for the doubly refined enumeration of alternating sign matrices

Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...

A polynomial method for the enumeration of plane partitions and alternating sign matrices

A formula for a doubly refined enumeration of alternating sign matrices

Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...

Affine Alternating Sign Matrices

An Alternating sign matrix is a square matrix of 0’s, 1’s, and −1’s in which the sum of the entries in each row or column is 1 and the signs of the nonzero entries in each row or column alternate. This paper attempts to define an analogue to alternating sign matrices which is infinite and periodic. After showing the analogue we define shares desirable cahracteristics with alternating sign matri...