"Alternating sign matrix theorem"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (→메타데이터) |
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| − | + | ==introduction== | |
| − | 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] | ||
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| − | + | ==lambda-determinant== | |
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| + | ==ASM== | ||
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| − | + | ==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 | ||
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| − | + | ==DPP to lattice paths== | |
| + | * P. Lalonde, Lattice paths and the antiautomorphism of the poset of descending plane partitions, Discrete Math. 271 (2003) 311–319 | ||
| + | * [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) | * lattice paths (lattice fermions) | ||
* related to [[non-intersecting paths]] | * related to [[non-intersecting paths]] | ||
| − | * Gessel-Viennot theorem | + | * Gessel-Viennot theorem |
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| − | + | ==from ASM to 6 vertex model with domain wall boundary condition(6VDW)== | |
* Kuperberg | * Kuperberg | ||
* Izergin - Korepin | * Izergin - Korepin | ||
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| − | + | ==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 | |
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| + | \phi(g,a)=\frac{1-g^2(1-a^2)}{ag}=q+q^{-1} | ||
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| + | ==history== | ||
* 1983 Mills, Robbins and Rumsey ASM conjecture | * 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 | * 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= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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| − | + | ==related items== | |
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| − | + | ==computational resource== | |
| + | * https://docs.google.com/file/d/0B8XXo8Tve1cxTVJuMk9keXA4cEE/edit | ||
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| + | ==encyclopedia== | ||
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 68번째 줄: | 101번째 줄: | ||
* http://en.wikipedia.org/wiki/Six-vertex_model | * http://en.wikipedia.org/wiki/Six-vertex_model | ||
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| − | + | ==books== | |
* [[2009년 books and articles|찾아볼 수학책]] | * [[2009년 books and articles|찾아볼 수학책]] | ||
| − | + | * R. J. Baxter [http://tpsrv.anu.edu.au/Members/baxter/book Exactly Solved Models in Statistical mechanics] | |
| − | * [http://tpsrv.anu.edu.au/Members/baxter/book Exactly Solved Models in Statistical mechanics] | + | * Proofs and Confirmations |
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| − | * Proofs and Confirmations | ||
** Bressoud, David M., | ** Bressoud, David M., | ||
** MAA Spectrum, Mathematical Associations of America, Washington, D.C., 1999. | ** MAA Spectrum, Mathematical Associations of America, Washington, D.C., 1999. | ||
| + | ** [[Proofs and Confirmation]] | ||
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| − | + | ==expositions== | |
| − | + | * [http://www.macalester.edu/%7Ebressoud/talks/ http://www.macalester.edu/~bressoud/talks/] | |
| + | * [http://www.macalester.edu/%7Ebressoud/talks/2009/asm-Moravian.pdf http://www.macalester.edu/~bressoud/talks/2009/asm-Moravian.pdf] | ||
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| + | ==articles== | ||
| + | * http://arxiv.org/abs/1512.06030 | ||
* [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] | ||
| − | * | + | * 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, | + | * How the alternating sign matrix conjecture was solved, |
** Bressoud, David M. and Propp, James, | ** Bressoud, David M. and Propp, James, | ||
** Notices of the American Mathematical Society, 46 (1999), 637-646. | ** Notices of the American Mathematical Society, 46 (1999), 637-646. | ||
| − | * Another proof of the alternating sign matrix conjecture | + | * Another proof of the alternating sign matrix conjecture |
** G Kuperberg, International Mathematics Research Notes (1996), 139-150. | ** G Kuperberg, International Mathematics Research Notes (1996), 139-150. | ||
| − | * Proof of the alternating sign matrix conjecture | + | * Proof of the alternating sign matrix conjecture |
** Zeilberger, Doron | ** Zeilberger, Doron | ||
** Electronic Journal of Combinatorics 3 (1996), R13. | ** Electronic Journal of Combinatorics 3 (1996), R13. | ||
| − | * [http://www.springerlink.com/content/tkg425gj56837471/ Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase] | + | * [http://www.springerlink.com/content/tkg425gj56837471/ Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase] |
** Bleher, Pavel M.; Fokin, Vladimir V. | ** Bleher, Pavel M.; Fokin, Vladimir V. | ||
| − | + | [[분류:개인노트]] | |
| − | + | [[분류:math and physics]] | |
| − | + | [[분류:math]] | |
| − | + | [[분류:migrate]] | |
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| − | * | + | ==메타데이터== |
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q3848436 Q3848436] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'alternating'}, {'LOWER': 'sign'}, {'LEMMA': 'matrix'}] | ||
2021년 2월 17일 (수) 02:55 기준 최신판
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=
computational resource
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.
- Proofs and Confirmation
expositions
- http://www.macalester.edu/~bressoud/talks/
- http://www.macalester.edu/~bressoud/talks/2009/asm-Moravian.pdf
articles
- http://arxiv.org/abs/1512.06030
- 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.
메타데이터
위키데이터
- ID : Q3848436
Spacy 패턴 목록
- [{'LOWER': 'alternating'}, {'LOWER': 'sign'}, {'LEMMA': 'matrix'}]