"Alternating sign matrix theorem"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
(피타고라스님이 이 페이지를 개설하였습니다.)
 
 
(사용자 3명의 중간 판 43개는 보이지 않습니다)
1번째 줄: 1번째 줄:
 +
==introduction==
  
 +
* 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]
 +
 +
 +
 +
 +
 +
==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
 +
* [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
 +
* 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==
 +
 +
 +
==computational resource==
 +
* https://docs.google.com/file/d/0B8XXo8Tve1cxTVJuMk9keXA4cEE/edit
 +
 +
 +
==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==
 +
 +
* [[2009년 books and articles|찾아볼 수학책]]
 +
* R. J. Baxter [http://tpsrv.anu.edu.au/Members/baxter/book 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/%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]
 +
 +
 +
 +
 +
 +
==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]
 +
* 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.
 +
* [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.
 +
 +
[[분류:개인노트]]
 +
[[분류:math and physics]]
 +
[[분류:math]]
 +
[[분류:migrate]]
 +
 +
==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



lambda-determinant

ASM

DPP



DPP to lattice paths





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

computational resource


encyclopedia




books


expositions



articles

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'alternating'}, {'LOWER': 'sign'}, {'LEMMA': 'matrix'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Alternating_sign_matrix_theorem&oldid=51856"