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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 432, Pages 5–29 (Mi znsl6107)  
This article is cited in 2 scientific papers (total in 2 papers)

Chip removal. Urban Renewal revisited

V. E. Aksenov, K. P. Kokhas

St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia
Full-text PDF (297 kB) Citations (2)
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Abstract: We describe a new combinatorial-algebraic transformation on graphs which we call “chip removal.” It generalizes the well-known Urban Renewal trick of Propp and Kuperberg. The chip removal is useful in calculations of determinants of adjacency matrices and matching numbers of graphs. A beautiful example of this technique is a theorem on removing four-contact chips, which generalizes Kuo's graphical condensation method. Numerous examples are given.
Key words and phrases: determinant of adjacency matrix, matching number, “Urban Renewal”, pfaffian, combinatorial linear algebra.
Received: 05.11.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 209, Issue 6, Pages 809–825
DOI: https://doi.org/10.1007/s10958-015-2528-9
Bibliographic databases:
Document Type: Article
UDC: 519.148
Language: Russian
Citation: V. E. Aksenov, K. P. Kokhas, “Chip removal. Urban Renewal revisited”, Representation theory, dynamical systems, combinatorial methods. Part XXIV, Zap. Nauchn. Sem. POMI, 432, POMI, St. Petersburg, 2015, 5–29; J. Math. Sci. (N. Y.), 209:6 (2015), 809–825
Citation in format AMSBIB
\Bibitem{AksKok15}
\by V.~E.~Aksenov, K.~P.~Kokhas
\paper Chip removal. Urban Renewal revisited
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 432
\pages 5--29
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6107}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 6
\pages 809--825
\crossref{https://doi.org/10.1007/s10958-015-2528-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84939433715}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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