Mathematics, Department of
Date of this Version
10-20-2017
Citation
2017 Author
Abstract
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.
Comments
the electronic journal of combinatorics 24(4) (2017), #P4.19