Domino tiling

introduction

• Aztec diamond
• random surface
• arctic circle phe
• rhombus tilings

 

 

 

mathematica code

1. detk[m_, n_] :=
    N[Product[
      Product[2 Cos[(Pi*l)/(m + 1)] + 2 I*Cos[(Pi*k)/(n + 1)], {k, 1,
        n}], {l, 1, m}], 10]
   Z[m_, n_] := Round[Sqrt[Abs[detk[m, n]]]]
   Z[8, 8]

 

 

 

amoeba

• http://www.cs.auckland.ac.nz/~mcw/Research/mvGF/asymultseq/Pema2010.pdf

 

 

Airy kernel

• random matrix
• random processes

 

 

 

character identities

• http://www.springerlink.com/content/k6350823632p86v2/

 

 

introductory problems

• http://2000clicks.com/mathhelp/PuzzleDominoTilingAnswer.aspx
• http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/June2006.html
• http://gurmeet.net/puzzles/tiling-with-calissons/
• Fibonacci numbers and 2xn rectangle domino tiling

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• non-intersecting paths

 

 

encyclopedia

• http://en.wikipedia.org/wiki/Aztec_diamond
• http://en.wikipedia.org/wiki/
• http://www.scholarpedia.org/
• http://www.proofwiki.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

books

• Winkler, Peter. 2003. Mathematical Puzzles: A Connoisseur’s Collection. A K Peters/CRC Press, 12월 26.
• 2010년 books and articles
  
• 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://ocw.mit.edu/courses/mathematics/18-312-algebraic-combinatorics-spring-2009/readings-and-lecture-notes/MIT18_312S09_Lecture32-36.pdf Musiker
• Cool Pictures in Probability , Sunil Chhita, September 18, 2008
• David, Guy, 와/과Carlos Tomei. 1989. “The Problem of the Calissons”. The American Mathematical Monthly 96 (5) (5월 1): 429-431. doi:10.2307/2325150.
• Math 192 lectures, topic by topic, J. Propp
• arctic phenomena in diamonds, groves and fortresses, or generating functions at work ,2008
• http://www.ams.org/programs/students/wwtbam/arl2009
• Planar Dimer Tilings
• Plane Tilings  Richard P. Stanley

 

articles

• Domino tilings of Aztec diamonds and squares
   
  Alternating-Sign Matrices and Domino Tilings (Part I)Noam Elkies, Greg Kuperberg, Michael Larsen and James Propp
  
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://arxiv.org/
• http://www.pdf-search.org/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://dx.doi.org/10.1023/A:1022420103267

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내
• The On-Line Encyclopedia of Integer Sequences
• http://functions.wolfram.com/