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Journal of Mathematical Sciences

, Volume 209, Issue 6, pp 809–825 | Cite as

Chip Removal. Urban Renewal Revisited

  • V. Aksenov
  • K. Kokhas
Article

We describe a new combinatorial-algebraic transformation on graphs which we call the “chip removal.” It generalizes the well-known urban renewal trick of Propp and Kuperberg. The chip removal is useful in calculations of the determinants of adjacency matrices and matching numbers of graphs. A beautiful example of applying this technique is a theorem on removing 4-contact chips, which generalizes Kuo’s graphical condensation method. Numerous examples are given. Bibliography: 6 titles.

Keywords

Adjacency Matrix Chebyshev Polynomial Urban Renewal Outgoing Edge Adjacency Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    V. Aksenov and K. Kokhas, “Domino tilings and determinants,” J. Math. Sci., 200, No. 6, 647–653 (2014).MATHCrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.ITMO UniversitySt.PetersburgRussia

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