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Zap. Nauchn. Sem. POMI, 2008, Volume 360, Pages 180–230 (Mi znsl2165)  

This article is cited in 3 scientific papers (total in 3 papers)

Domino tilings of aztec diamonds and squares

K. Kokhas

Saint-Petersburg State University

Abstract: The article gives several new combinatorial proofs of well-known theorems about domino tilings of aztec diamonds and squares. We prove also generalizations of these theorems for the generating polynomials of some statistics of tilings. Some results here are new, for example, we describe how to calculate the rank of a tiling using special weights of edges on the square grid.
The text is self-sufficient, we give numerous illustrations to all combinatorial constructions. Bibl. – 17 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 158:6, 868–894

Bibliographic databases:

UDC: 519.148
Received: 19.11.2008

Citation: K. Kokhas, “Domino tilings of aztec diamonds and squares”, Representation theory, dynamics systems, combinatorial methods. Part XVI, Zap. Nauchn. Sem. POMI, 360, POMI, St. Petersburg, 2008, 180–230; J. Math. Sci. (N. Y.), 158:6 (2009), 868–894

Citation in format AMSBIB
\Bibitem{Kok08}
\by K.~Kokhas
\paper Domino tilings of aztec diamonds and squares
\inbook Representation theory, dynamics systems, combinatorial methods. Part~XVI
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 360
\pages 180--230
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2165}
\zmath{https://zbmath.org/?q=an:1180.05027}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 158
\issue 6
\pages 868--894
\crossref{https://doi.org/10.1007/s10958-009-9421-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349122700}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Aksenov, K. Kokhas, “Domino tilings and determinants”, J. Math. Sci. (N. Y.), 200:6 (2014), 647–653  mathnet  crossref
    2. O. V. Bursian, “Chip removal for computing the number of perfect matchings”, J. Math. Sci. (N. Y.), 216:1 (2016), 41–52  mathnet  crossref  mathscinet
    3. Fendler M., Grieser D., “A New Simple Proof of the Aztec Diamond Theorem”, Graphs Comb., 32:4 (2016), 1389–1395  crossref  mathscinet  zmath  isi  scopus
  • Записки научных семинаров ПОМИ
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