Geodesic
Perfect matchings of trimmed Aztec rectangles
Tri Lai1
1University of Nebraska - Lincoln
The electronic journal of combinatorics, Tome 24 (2017) no. 4
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We consider several new families of subgraphs of the square grid whose matchings are enumerated by powers of several small prime numbers: $2$, $3$, $5$, and $11$. Our graphs are obtained by trimming two opposite corners of an Aztec rectangle. The result yields a proof of a conjecture posed by Ciucu. In addition, we reveal a hidden connection between our graphs and the hexagonal dungeons introduced by Blum.
DOI : 10.37236/6440
Classification : 05A15, 05B45, 05C30
Mots-clés : perfect matching, tiling, dual graph, Aztec rectangle, graphical condensation, hexagonal dungeon

Tri Lai  1

1 University of Nebraska - Lincoln 
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     author = {Tri Lai},
     title = {Perfect matchings of trimmed {Aztec} rectangles},
     journal = {The electronic journal of combinatorics},
     year = {2017},
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     number = {4},
     doi = {10.37236/6440},
     zbl = {1373.05011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6440/}
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Tri Lai. Perfect matchings of trimmed Aztec rectangles. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/6440

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