Abstract
We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing its center. W. Jockusch and J. Propp (in an unpublished work) found that the number of tilings of quartered Aztec diamonds is given by simple product formulas. In this paper we present a simple proof for this result.
Highlights
Propp found that the number of tilings of quartered Aztec diamonds is given by simple product formulas
In this paper we present a simple proof for this result
In this paper a region is a connected union of unit squares in the square lattice
Summary
In this paper a (lattice) region is a connected union of unit squares in the square lattice. The number of tilings of a quartered Aztec diamond is given by the theorem stated below. One can remove some forced edges and the vertices incident to them from a graph to get a new graph with the same number of perfect matchings.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
