Enumeration of Tilings of Diamonds and Hexagons with Defects
نویسنده
چکیده
We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we obtain solutions to open problems 1, 2, and 10 in James Propp’s list of problems on enumeration of matchings [22].
منابع مشابه
Alternating sign matrices and tilings of Aztec rectangles
The problem of counting numbers of tilings of certain regions has long interested researchers in a variety of disciplines. In recent years, many beautiful results have been obtained related to the enumeration of tilings of particular regions called Aztec diamonds. Problems currently under investigation include counting the tilings of related regions with holes and describing the behavior of ran...
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