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Rhombus Tilings of a Hexagon with Three Fixed Border Tiles

Theresia Eisenkölbl
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Abstract

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.

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Theresia Eisenkölbl. 1998-09-08. Rhombus Tilings of a Hexagon with Three Fixed Border Tiles. https://arxiv.org/abs/math/9712261

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