Enumerative combinatorics
American Mathematical Monthly
Lattice path proofs for determinantal formulas for symplectic and orthogonal characters
Journal of Combinatorial Theory Series A
Enumeration of Lozenge Tilings of hexagons with a central triangular hole
Journal of Combinatorial Theory Series A
Enumeration of Lozenge tilings of hexagons with cut-off corners
Journal of Combinatorial Theory Series A
Proof of the Razumov-Stroganov conjecture
Journal of Combinatorial Theory Series A
Fully Packed Loop configurations in a triangle
Journal of Combinatorial Theory Series A
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Two conjectures of Zuber (On the counting of fully packed loops configurations. Some new conjectures, Electronic J. Combin 11 (2004)) on the enumeration of configurations in the fully packed loop model on the square grid with periodic boundary conditions, which have a prescribed linkage pattern, are proved. Following an idea of de Gier (Loops, matchings and alternating-sign matrices, Discrete Math., to appear), the proofs are based on bijections between such fully packed loop configurations and rhombus tilings, and the hook-content formula for semistandard tableaux.