Enumeration of Lozenge tilings of hexagons with cut-off corners

Authors:
Mihai Ciucu;Christian Krattenthaler
Affiliations:
Georgia Institute of Technology, School of Mathematics, Atlanta, Georgia;Institut für Mathematik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

Citing 7
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Abstract

Motivated by the enumeration of a class of plane partitions studied by Proctor and by considerations about symmetry classes of plane partitions, we consider the problem of enumerating lozenge tilings of a hexagon with "maximal staircases" removed from some of its vertices. The case of one vertex corresponds to Proctor's problem. For two vertices there are several cases to consider, and most of them lead to nice enumeration formulas. For three or more vertices there do not seem to exist nice product formulas in general, but in one special situation a lot of factorization occurs, and we pose the problem of finding a formula for the number of tilings in this case.