Content deleted Content added
→Alternating sign matrix conjecture: -> →Alternating sign matrix theorem: : confusing name for a theorem |
→Razumov–Stroganov conjecture: -> →Razumov–Stroganov problem: : this is not a conjecture, as it is proven |
||
Line 70:
This theorem 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 due to Anatoli Izergin.<ref>"Determinant formula for the six-vertex model", A. G. Izergin et al. 1992 ''J. Phys. A'': Math. Gen. 25 4315.</ref> A third proof was given by [[Ilse Fischer]] using what is called the ''operator method''.<ref>{{Cite journal|last=Fischer|first=Ilse|title=A new proof of the refined alternating sign matrix theorem|journal=Journal of Combinatorial Theory, Series A|year=2005|volume=114|issue=2|pages=253–264|doi=10.1016/j.jcta.2006.04.004|arxiv=math/0507270|bibcode=2005math......7270F}}</ref>
==Razumov–Stroganov
In 2001, A. Razumov and Y. Stroganov conjectured a connection between O(1) loop model, fully packed loop model (FPL) and ASMs.<ref>Razumov, A.V., Stroganov Yu.G., [https://arxiv.org/abs/cond-mat/0012141 Spin chains and combinatorics], ''Journal of Physics A'', '''34''' (2001), 3185-3190.</ref>
| |||