Alternating sign matrix theorem

introduction

• PDF
• 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

 

 

 

 

 

 

 

 

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 http://qchu.wordpress.com/2009/11/17/the-lindstrom-gessel-viennot-lemma/

 

 

 

from ASM to 6 vertex model with domain wall boundary condition

• 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
• 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=

 

 

 

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

• http://arxiv.org/