Enumeration of Lozenge Tilings of Hexagons with Cut-Off Corners
Copyright policy )Enumeration of Lozenge Tilings of Hexagons with Cut-Off Corners
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.
23 pages, AmS-TeX
- University of Vienna Austria
- MEDIZINISCHE UNIVERSITAT GRAZ Austria
- Georgia Institute of Technology School of Mathematics United States
- Georgia Institute of Technology United States
- GEORGIA TECH RESEARCH CORPORATION United States
non-intersecting lattice paths, tiling enumeration, Exact enumeration problems, generating functions, 05A15, 05A17, 05B45 (Primary) 11P81, 52C20 (Secondary), Tilings in \(2\) dimensions (aspects of discrete geometry), Theoretical Computer Science, lozenge tilings, plane partitions, Computational Theory and Mathematics, Combinatorial aspects of tessellation and tiling problems, FOS: Mathematics, perfect matchings., Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), determinant evaluations, symmetry classes
non-intersecting lattice paths, tiling enumeration, Exact enumeration problems, generating functions, 05A15, 05A17, 05B45 (Primary) 11P81, 52C20 (Secondary), Tilings in \(2\) dimensions (aspects of discrete geometry), Theoretical Computer Science, lozenge tilings, plane partitions, Computational Theory and Mathematics, Combinatorial aspects of tessellation and tiling problems, FOS: Mathematics, perfect matchings., Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), determinant evaluations, symmetry classes
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