The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. I (Q1272360)
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| Language | Label | Description | Also known as |
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| English | The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. I |
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The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis. I (English)
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2 August 1999
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Let be given a hexagon in the plane from the regular triangular lattice with sides \(a,b,c,a,b,c\). A classic result of MacMahon gives a product formula for the number of rhombus tilings of this hexagon. The present paper solves a refined enumeration problem: what is the number of rhombus tilings that contain the \(\ell\)th rhombus on the symmetry axis of the hexagon. From the closed form an asymptotic formula is also derived.
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lozenge tilings
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plane partitions
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nonintersecting lattice paths
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matchings factorization
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determinant evaluations
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hexagon
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rhombus tilings
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enumeration problem
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