"Domino tiling"의 두 판 사이의 차이
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* arctic circle phe | * arctic circle phe | ||
* rhombus tilings | * rhombus tilings | ||
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| + | <h5>mathematica code</h5> | ||
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| + | # detk[m_, n_] :=<br> N[Product[<br> Product[2 Cos[(Pi*l)/(m + 1)] + 2 I*Cos[(Pi*k)/(n + 1)], {k, 1,<br> n}], {l, 1, m}], 10]<br> Z[m_, n_] := Round[Sqrt[Abs[detk[m, n]]]]<br> Z[8, 8] | ||
| 106번째 줄: | 115번째 줄: | ||
<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5> | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5> | ||
| − | * Domino tilings of Aztec diamonds and squares<br> | + | * Domino tilings of Aztec diamonds and squares<br> <br>[http://dx.doi.org/10.1023/A:1022420103267 Alternating-Sign Matrices and Domino Tilings (Part I)]Noam Elkies, Greg Kuperberg, Michael Larsen and James Propp<br> |
* http://www.ams.org/mathscinet | * http://www.ams.org/mathscinet | ||
* http://www.zentralblatt-math.org/zmath/en/ | * http://www.zentralblatt-math.org/zmath/en/ | ||
2011년 8월 8일 (월) 05:33 판
introduction
- Aztec diamond
- random surface
- arctic circle phe
- rhombus tilings
mathematica code
- 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
Airy kernel
character identities
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
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)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field