Rhombus Tilings of a Hexagon with Three Fixed Border Tiles
Copyright policy )Rhombus Tilings of a Hexagon with Three Fixed Border Tiles
We compute the number of rhombus tilings of a hexagon with sides $a+2,b+2,c+2,a+2,b+2,c+2$ with three fixed tiles touching the border. The particular case $a=b=c$ solves a problem posed by Propp. Our result can also be viewed as the enumeration of plane partitions having $a+2$ rows and $b+2$ columns, with largest entry $\le c+2$, with a given number of entries $c+2$ in the first row, a given number of entries 0 in the last column and a given bottom-left entry.
7 pages, AmS-LaTeX, uses TeXDraw; revised version which is to appear in J. Combin. Theory Ser. A
- Univesität Wien Austria
- MEDIZINISCHE UNIVERSITAT GRAZ Austria
- Universität Wien Austria
- Universität Wien Austria
- University of Vienna Austria
05A15 05B45 52C20, Exact enumeration problems, generating functions, determinants, Dodgson's condensation rule, Tilings in \(2\) dimensions (aspects of discrete geometry), enumeration, Theoretical Computer Science, lozenge tilings, plane partitions, Computational Theory and Mathematics, Combinatorial aspects of tessellation and tiling problems, nonintersecting lattice paths, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), rhombus tilings, Combinatorial identities, bijective combinatorics
05A15 05B45 52C20, Exact enumeration problems, generating functions, determinants, Dodgson's condensation rule, Tilings in \(2\) dimensions (aspects of discrete geometry), enumeration, Theoretical Computer Science, lozenge tilings, plane partitions, Computational Theory and Mathematics, Combinatorial aspects of tessellation and tiling problems, nonintersecting lattice paths, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), rhombus tilings, Combinatorial identities, bijective combinatorics
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