Proof of two conjectures of Zuber on fully packed loop configurations
Caselli, F. ; Krattenthaler, C.
arXiv, 0312217 / Harvested from arXiv
Text on arXiv
Two conjectures of Zuber [``On the counting of fully packed loops configurations. Some new conjectures,'' preprint] 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.
Publié le : 2003-12-10
Classification:  Mathematics - Combinatorics,  Condensed Matter - Statistical Mechanics,  Mathematical Physics,  Primary 05A15,  Secondary 05B45 05E05 05E10 82B23 
@article{0312217,
     author = {Caselli, F. and Krattenthaler, C.},
     title = {Proof of two conjectures of Zuber on fully packed loop configurations},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0312217}
}

Caselli, F.; Krattenthaler, C. Proof of two conjectures of Zuber on fully packed loop configurations. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0312217/