A new proof of the refined alternating sign matrix theorem

Authors:
Ilse Fischer
Affiliations:
Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 3
Cited 6

Proofs and confirmations: the story of the alternating sign matrix conjecture

Proofs and confirmations: the story of the alternating sign matrix conjecture
Concrete Math

Concrete Math
Descending plane partitions and rhombus tilings of a hexagon with a triangular hole

European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures

An operator formula for the number of halved monotone triangles with prescribed bottom row

Journal of Combinatorial Theory Series A
The operator formula for monotone triangles - simplified proof and three generalizations

Journal of Combinatorial Theory Series A
Refined enumerations of alternating sign matrices: monotone (d,m)-trapezoids with prescribed top and bottom row

Journal of Algebraic Combinatorics: An International Journal
On the weighted enumeration of alternating sign matrices and descending plane partitions

Journal of Combinatorial Theory Series A
Linear relations of refined enumerations of alternating sign matrices

Journal of Combinatorial Theory Series A
A doubly-refined enumeration of alternating sign matrices and descending plane partitions

Journal of Combinatorial Theory Series A

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the early 1980s, Mills, Robbins and Rumsey conjectured, and in 1996 Zeilberger proved a simple product formula for the number of nxn alternating sign matrices with a 1 at the top of the ith column. We give an alternative proof of this formula using our operator formula for the number of monotone triangles with prescribed bottom row. In addition, we provide the enumeration of certain 0-1-(-1) matrices generalizing alternating sign matrices.