Annals of Combinatorics 2 (1998) 19-41

The Number of Rhombus Tilings of a Symmetric Hexagon which Contain a Fixed Rhombus on the Symmetry Axis, I

M. Fulmek1 and C. Krattenthaler2

Institut für Mathematik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria

Received December 23, 1997

AMS Subject Classification: 05A15; 05A17,05A19, 05B45,33C20, 52C20

Abstract. We compute the number of rhombus tilings of a hexagon with sides N,M,N,N,M,N, which contain a fixed rhombus on the symmetry axis that cuts through the sides of length M.

Keywords: matchings factorization theorem, rhombus tilings, lozenge tilings, plane partitions, nonintersecting lattice paths, determinant evaluations


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