"Alternating sign matrix theorem"의 두 판 사이의 차이
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| 25번째 줄: | 25번째 줄: | ||
[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, 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, 2006 | ||
| − | Rhombus tilings/Dimers or Lattice Paths for DPPs | + | * 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/ | ||
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| 39번째 줄: | 38번째 줄: | ||
<h5>from ASM to 6 vertex model</h5> | <h5>from ASM to 6 vertex model</h5> | ||
| − | Kuperberg | + | * Kuperberg |
| − | + | * Izergin - Korepin | |
| − | Izergin - Korepin | ||
| 51번째 줄: | 49번째 줄: | ||
<h5>history</h5> | <h5>history</h5> | ||
| − | * 1983 | + | * 1983 Mills, Robbins and Rumsey ASM conjecture |
| − | * 1996 Kuperberg | + | * 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= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
2012년 1월 31일 (화) 09:21 판
introduction
descending plane partitions and alternating sign matrix http://math.berkeley.edu/~reshetik/RTG-semin-fall-2010/Philippe.pdf
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}
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
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=
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Plane_partition
- http://en.wikipedia.org/wiki/alternating_sign_matrix
- http://en.wikipedia.org/wiki/Six-vertex_model
- 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
- 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://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
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.
- 논문정리
- http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/