Rhombus Tilings of a Hexagon with Three Fixed Border Tiles

Theresia Eisenkölbl


We compute the number of rhombus tilings of a hexagon with sides a,b,c,a,b,c 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 rows and b columns, with largest entry smaller or equal to c, with a given number of entries equal to c in the first row, a given number of entries equal to 0 in the last column and a given bottom-left entry. (6 pages)

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Last modified: 20. April 2000