9 citations · 9 across the 1 of their papers we have counts for
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Tilings of hexagons with a removed triad of bowties
Mihai Ciucu, Tri Lai, Ranjan Rohatgi
In this paper we consider arbitrary hexagons on the triangular lattice with three arbitrary bowtie-shaped holes, whose centers form an equilateral triangle. The number of lozenge t…
A shuffling theorem for lozenge tilings of doubly-dented hexagons
Tri Lai, Ranjan Rohatgi
MacMahon's theorem on plane partitions yields a simple product formula for tiling number of a hexagon, and Cohn, Larsen and Propp's theorem provides an explicit enumeration for til…
A New [Combinatorial] Proof of the Commutativity of Matching Polynomials for Cycles
Garner Cochran, Corbin Groothuis, Andrew Herring +2
We prove some functional equations involving the (classical) matching polynomials of path and cycle graphs and the -matching polynomial of a cycle graph. A matching in a (finite…
Cyclically Symmetric Lozenge Tilings of a Hexagon with Four Holes
Tri Lai, Ranjan Rohatgi
The work of Mills, Robbins, and Rumsey on cyclically symmetric plane partitions yields a simple product formula for the number of lozenge tilings of a regular hexagon, which are in…