Two conjectures of Zuber [On the counting of fully packed loops configurations. Some new conjectures, Electronic J. Combin. 11 (2004), R13] 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.
F. Caselli, C. Krattenthaler (2004). Proof of two conjectures of Zuber on fully packed loop configurations. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 108, 123-146 [10.1016/j.jcta.2004.06.006].
Proof of two conjectures of Zuber on fully packed loop configurations
CASELLI, FABRIZIO;
2004
Abstract
Two conjectures of Zuber [On the counting of fully packed loops configurations. Some new conjectures, Electronic J. Combin. 11 (2004), R13] 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
