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A Generalization of Aztec Dragons

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Abstract

Aztec dragons are lattice regions first introduced by James Propp, which have the number of tilings given by a power of 2. This family of regions has been investigated further by a number of authors. In this paper, we consider a generalization of the Aztec dragons to two new families of 6-sided regions. By using Kuo’s graphical condensation method, we prove that the tilings of the new regions are always enumerated by powers of 2 and 3.

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Notes

  1. The unit here is the smallest distance between the centers of two hexagonal fundamental regions in the dragon lattice, i.e the unit of the above triangular lattice.

  2. This software is available at http://dwilson.com/vaxmacs.

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Acknowledgments

This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation (Grant No. DMS-0931945). The author would like to thank the anonymous referee for his/her careful reading and helpful comments.

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  1. Institute for Mathematics and its Applications, Minneapolis, MN, 55455, USA

    Tri Lai

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  1. Tri Lai
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Correspondence to Tri Lai.

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Lai, T. A Generalization of Aztec Dragons. Graphs and Combinatorics 32, 1979–1999 (2016). https://doi.org/10.1007/s00373-016-1691-1

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  • DOI: https://doi.org/10.1007/s00373-016-1691-1

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