"Alternating sign matrix theorem"의 두 판 사이의 차이

2012년 1월 31일 (화) 08:26 판

introduction

PDF
descending plane partitions and alternating sign matrix [1]http://math.berkeley.edu/~reshetik/RTG-semin-fall-2010/Philippe.pdf [2]
Refined enumeration of Alternating Sign Matrices and Descending Plane Partitions

lambda-determinant

ASM

DPP

DPP to lattice paths

P. Lalonde, Lattice paths and the antiautomorphism of the poset of descending plane partitions, Discrete Math. 271 (2003) 311–319

Descending plane partitions and rhombus tilings of a hexagon with a triangular hole C. Krattenthaler, 2006

Rhombus tilings/Dimers or Lattice Paths for DPPs
lattice paths (lattice fermions)
related to non-intersecting paths
Gessel-Viennot theorem http://qchu.wordpress.com/2009/11/17/the-lindstrom-gessel-viennot-lemma/

from ASM to 6 vertex model

Kuperberg
Izergin - Korepin

1+1 dimensional Lorentzian quantum gravity

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}

history

1983 Mills, Robbins and Rumsey ASM conjecture
1996 Kuperberg alternative proof of ASM conjecture using the connection with the six vertex model
http://www.google.com/search?hl=en&tbs=tl:1&q=

related items

encyclopedia

http://ko.wikipedia.org/wiki/
http://en.wikipedia.org/wiki/
http://en.wikipedia.org/wiki/
http://en.wikipedia.org/wiki/
Princeton companion to mathematics(Companion_to_Mathematics.pdf)

books

찾아볼 수학책

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.

expositions

http://www.macalester.edu/~bressoud/talks/

http://www.macalester.edu/~bressoud/talks/2009/asm-Moravian.pdf

articles

http://www.math.lsa.umich.edu/~lserrano/asm.pdf
Propp, James. 2002. The many faces of alternating-sign matrices. math/0208125 (August 15). http://arxiv.org/abs/math/0208125.
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.

experts on the field

http://arxiv.org/

@@ 1번째 줄: / 1번째 줄: @@
 <h5>introduction</h5>
-PDF
+* PDF
+* descending plane partitions and alternating sign matrix  [http://math.berkeley.edu/%7Ereshetik/RTG-semin-fall-2010/Philippe.pdf ][http://math.berkeley.edu/%7Ereshetik/RTG-semin-fall-2010/Philippe.pdf http://math.berkeley.edu/~reshetik/RTG-semin-fall-2010/Philippe.pdf][http://math.berkeley.edu/%7Ewilliams/combinatorics/zj.html ]
+* [http://math.berkeley.edu/%7Ewilliams/combinatorics/zj.html Refined enumeration of Alternating Sign Matrices and Descending Plane Partitions]
-descending plane partitions and alternating sign matrix  [http://math.berkeley.edu/%7Ereshetik/RTG-semin-fall-2010/Philippe.pdf http://math.berkeley.edu/~reshetik/RTG-semin-fall-2010/Philippe.pdf]
+<h5>lambda-determinant</h5>
@@ 9번째 줄: / 15번째 줄: @@
-<h5>1+1 dimensional Lorentzian quantum gravity</h5>
+<h5>ASM</h5>
-exists quantities \phi such that if \phi(g,a)=\phi'(g',a') then [T(a,g),T(a',g')]=0
+<h5>DPP</h5>
-\phi(g,a)=\frac{1-g^2(1-a^2)}{ag}=q+q^{-1}
@@ 40번째 줄: / 54번째 줄: @@
 * Kuperberg
 * Izergin - Korepin
+<h5>1+1 dimensional Lorentzian quantum gravity</h5>
+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}