"Alternating sign matrix theorem"의 두 판 사이의 차이

수학노트
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잔글 (찾아 바꾸기 – “분류:개인노트분류:개인노트” 문자열을 “분류:개인노트” 문자열로)
 
(사용자 2명의 중간 판 10개는 보이지 않습니다)
2번째 줄: 2번째 줄:
  
 
* PDF
 
* PDF
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* 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 ]
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* 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]
 
* [http://math.berkeley.edu/%7Ewilliams/combinatorics/zj.html Refined enumeration of Alternating Sign Matrices and Descending Plane Partitions]
  
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==lambda-determinant==
 
==lambda-determinant==
  
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==ASM==
 
==ASM==
  
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==DPP==
 
==DPP==
31번째 줄: 31번째 줄:
 
* number of ASM of size n is same as the above sequence
 
* number of ASM of size n is same as the above sequence
  
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==DPP to lattice paths==
 
==DPP to lattice paths==
44번째 줄: 44번째 줄:
 
* Gessel-Viennot theorem
 
* Gessel-Viennot theorem
  
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==from ASM to 6 vertex model with domain wall boundary condition(6VDW)==
 
==from ASM to 6 vertex model with domain wall boundary condition(6VDW)==
57번째 줄: 57번째 줄:
 
* Izergin - Korepin
 
* Izergin - Korepin
  
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==1+1 dimensional Lorentzian quantum gravity==
 
==1+1 dimensional Lorentzian quantum gravity==
67번째 줄: 67번째 줄:
 
\phi(g,a)=\frac{1-g^2(1-a^2)}{ag}=q+q^{-1}
 
\phi(g,a)=\frac{1-g^2(1-a^2)}{ag}=q+q^{-1}
  
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==history==
 
==history==
83번째 줄: 83번째 줄:
 
* 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==
 
==related items==
  
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==computational resource==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxTVJuMk9keXA4cEE/edit
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==encyclopedia==
 
==encyclopedia==
98번째 줄: 101번째 줄:
 
* http://en.wikipedia.org/wiki/Six-vertex_model
 
* http://en.wikipedia.org/wiki/Six-vertex_model
  
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==books==
 
==books==
108번째 줄: 111번째 줄:
 
* [[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]
 
* R. J. Baxter [http://tpsrv.anu.edu.au/Members/baxter/book Exactly Solved Models in Statistical mechanics]
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*  Proofs and Confirmations<br>
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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.
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** [[Proofs and Confirmation]]
  
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* http://gigapedia.info/1/
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
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==expositions==
 
==expositions==
127번째 줄: 123번째 줄:
 
* [http://www.macalester.edu/%7Ebressoud/talks/2009/asm-Moravian.pdf http://www.macalester.edu/~bressoud/talks/2009/asm-Moravian.pdf]
 
* [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==
 
==articles==
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* 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]
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* Propp, James. 2002. The many faces of alternating-sign matrices. math/0208125 (August 15). http://arxiv.org/abs/math/0208125. 
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* Propp, James. 2002. The many faces of alternating-sign matrices. math/0208125 (August 15). http://arxiv.org/abs/math/0208125.  
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*  How the alternating sign matrix conjecture was solved,<br>
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*  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.
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*  Another proof of the alternating sign matrix conjecture<br>
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*  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.
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*  Proof of the alternating sign matrix conjecture<br>
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*  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.
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* [http://www.springerlink.com/content/tkg425gj56837471/ Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase]<br>
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* [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.
  
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* [[2010년 books and articles|논문정리]]
 
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* http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
 
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* http://www.ams.org/mathscinet
 
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* http://www.zentralblatt-math.org/zmath/en/
 
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* http://pythagoras0.springnote.com/
 
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
 
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* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 
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* 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=
 
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* http://dx.doi.org/
 
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==experts on the field==
 
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* http://arxiv.org/
 
 
[[분류:개인노트]]
 
[[분류:개인노트]]
 
[[분류:math and physics]]
 
[[분류:math and physics]]
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[[분류:math and physics]]
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[[분류:math]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q3848436 Q3848436]
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===Spacy 패턴 목록===
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* [{'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"