"Alternating sign matrix theorem"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| − | + | ==introduction</h5> | |
* PDF | * PDF | ||
| 9번째 줄: | 9번째 줄: | ||
| − | + | ==lambda-determinant</h5> | |
| 17번째 줄: | 17번째 줄: | ||
| − | + | ==ASM</h5> | |
| 25번째 줄: | 25번째 줄: | ||
| − | + | ==DPP</h5> | |
* http://mathworld.wolfram.com/DescendingPlanePartition.html | * http://mathworld.wolfram.com/DescendingPlanePartition.html | ||
| 35번째 줄: | 35번째 줄: | ||
| − | + | ==DPP to lattice paths</h5> | |
* P. Lalonde, Lattice paths and the antiautomorphism of the poset of descending plane partitions, Discrete Math. 271 (2003) 311–319 | * P. Lalonde, Lattice paths and the antiautomorphism of the poset of descending plane partitions, Discrete Math. 271 (2003) 311–319 | ||
| 52번째 줄: | 52번째 줄: | ||
| − | + | ==from ASM to 6 vertex model with domain wall boundary condition(6VDW)</h5> | |
* Kuperberg | * Kuperberg | ||
| 61번째 줄: | 61번째 줄: | ||
| − | + | ==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 | exists quantities \phi such that if \phi(g,a)=\phi'(g',a') then [T(a,g),T(a',g')]=0 | ||
| 73번째 줄: | 73번째 줄: | ||
| − | + | ==history</h5> | |
* 1983 Mills, Robbins and Rumsey ASM conjecture | * 1983 Mills, Robbins and Rumsey ASM conjecture | ||
| 87번째 줄: | 87번째 줄: | ||
| − | + | ==related items</h5> | |
| − | + | ==encyclopedia</h5> | |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 104번째 줄: | 104번째 줄: | ||
| − | + | ==books</h5> | |
* [[2009년 books and articles|찾아볼 수학책]] | * [[2009년 books and articles|찾아볼 수학책]] | ||
| 122번째 줄: | 122번째 줄: | ||
| − | + | ==expositions</h5> | |
* [http://www.macalester.edu/%7Ebressoud/talks/ http://www.macalester.edu/~bressoud/talks/] | * [http://www.macalester.edu/%7Ebressoud/talks/ http://www.macalester.edu/~bressoud/talks/] | ||
| 131번째 줄: | 131번째 줄: | ||
| − | + | ==articles</h5> | |
* [http://www.math.lsa.umich.edu/%7Elserrano/asm.pdf http://www.math.lsa.umich.edu/~lserrano/asm.pdf] | * [http://www.math.lsa.umich.edu/%7Elserrano/asm.pdf http://www.math.lsa.umich.edu/~lserrano/asm.pdf] | ||
| 160번째 줄: | 160번째 줄: | ||
| − | + | ==experts on the field</h5> | |
* http://arxiv.org/ | * http://arxiv.org/ | ||
2012년 10월 28일 (일) 12:51 판
==introduction
- 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
- http://mathworld.wolfram.com/DescendingPlanePartition.html
- number of DPPs with parts at most n is given by Andrews in 1979.
- number of ASM of size n is same as the above sequence
==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
==from ASM to 6 vertex model with domain wall boundary condition(6VDW)
- 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
- 198? Korepin recurrence relation for 6VDW
- 1987 Izergin. determinant function of the partition function of the 6VDW based on Korepin's work
- 1996 Zilberger proof of ASM conjecture
- 1996 Kuperberg alternative proof of ASM conjecture using the connection with the six vertex model
- 2011 correspondence between DPP and ASM
- http://www.google.com/search?hl=en&tbs=tl:1&q=
==related items
==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
==books
- 찾아볼 수학책
- R. J. Baxter Exactly Solved Models in Statistical mechanics
- 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/
==experts on the field