"Alternating sign matrix theorem"의 두 판 사이의 차이

2010년 12월 1일 (수) 08:23 판

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exists quantities \phi such that if \phi(g,a)=\phi'(g',a') then [T(a,g),T(a',g')]=0

\phi(g,a)=\frac{1-g^2(1-a^2)}{ag}=q+q^{-1}

Lalonde 2003

Rhombus tilings/Dimers or Lattice Paths for DPPs

lattice paths (lattice fermions)

Gessel-Viennot theorem

Exactly Solved Models in Statistical mechanics
- R. J. Baxter
Proofs and Confirmations
- Bressoud, David M.,
- MAA Spectrum, Mathematical Associations of America, Washington, D.C., 1999.

http://www.math.lsa.umich.edu/~lserrano/asm.pdf
How the alternating sign matrix conjecture was solved,
- Bressoud, David M. and Propp, James,
- Notices of the American Mathematical Society, 46 (1999), 637-646.
Another proof of the alternating sign matrix conjecture
- G Kuperberg, International Mathematics Research Notes (1996), 139-150.
Proof of the alternating sign matrix conjecture
- Zeilberger, Doron
- Electronic Journal of Combinatorics 3 (1996), R13.
Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
- Bleher, Pavel M.; Fokin, Vladimir V.

@@ 23번째 줄: / 23번째 줄: @@
 Lalonde 2003
-Krattenthaler 2006
+[http://dx.doi.org/10.1016/j.ejc.2006.06.008 Descending plane partitions and rhombus tilings of a hexagon with a triangular hole]C. Krattenthaler
 Rhombus tilings/Dimers or Lattice Paths for DPPs
@@ 29번째 줄: / 29번째 줄: @@
 lattice paths (lattice fermions)
+related to [[non-intersecting paths]]
+Gessel-Viennot theorem