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no. 4
Ehrhart theory on periodic graphs
Inoue, Takuya1; Nakamura, Yusuke2
1 Graduate School of Mathematical Sciences the University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo 153-8914 Japan
2 Graduate School of Mathematics Nagoya University Furo-cho Chikusa-ku Nagoya 464-8602 Japan
Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 969-1010.

The purpose of this paper is to extend the scope of Ehrhart theory to periodic graphs. We give sufficient conditions for the growth sequences of periodic graphs to be a quasi-polynomial and to satisfy the reciprocity laws. Furthermore, we apply our theory to determine the growth series in several new examples.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.367
Classification: 05A15, 52B20, 05C30, 92E10
Keywords: Ehrhart theory, periodic graphs, tiling problems, generating functions, coordination sequences, growth sequences

Inoue, Takuya 1; Nakamura, Yusuke 2

1 Graduate School of Mathematical Sciences the University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo 153-8914 Japan
2 Graduate School of Mathematics Nagoya University Furo-cho Chikusa-ku Nagoya 464-8602 Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Inoue, Takuya; Nakamura, Yusuke. Ehrhart theory on periodic graphs. Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 969-1010. doi : 10.5802/alco.367. https://alco.centre-mersenne.org/articles/10.5802/alco.367/

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