Alternating sign matrix: Difference between revisions

Revision as of 16:43, 8 May 2013

Revision as of 18:36, 22 June 2013

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==Example==

An example of aan alternating sign matrix (that is not also a permutation matrix) is

[[File:Matrice signes alternants 4x4.svg|thumbnail|Puzzle picture]]

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:[[1 (number)|1]], 1, [[2 (number)|2]], [[7 (number)|7]], [[42 (number)|42]], 429, 7436, 218348, … {{OEIS|id=A005130}}.

This conjecture was first proved by [[Doron Zeilberger]] in 1992.<ref>Zeilberger, Doron, [http://www.combinatorics.org/Volume_3/Abstracts/v3i2r13.html Proof of the alternating sign matrix conjecture], ''[http://www.combinatorics.org/ Electronic Journal of Combinatorics]'' 3 (1996), R13.</ref> In 1995, [[Greg Kuperberg]] gave a short proof<ref>[[Greg Kuperberg|Kuperberg, Greg]], [http://front.math.ucdavis.edu/math.CO/9712207 Another proof of the alternating sign matrix conjecture], ''International Mathematics Research Notes'' (1996), 139-150.</ref> based on the [[Yang-Baxter equation]] for the six vertex model with ___domain wall boundary conditions, that uses a determinant calculation,<ref>Determinant formula for the six-vertex model, A. G. Izergin et. al. 1992 J. Phys. A: Math. Gen. 25 4315.</ref> which solves recurrence relations due to [[Vladimir Korepin]].<ref>V. E. Korepin, [http://projecteuclid.org/euclid.cmp/1103921777 Calculation of norms of Bethe wave functions], Comm. Math. Phys. Volume 86, Number 3 (1982), 391-418.</ref>

==Razumov–Stroganov conjecture==