We propose the first algebraic determinantal formula to enumerate tilings of a centro-symmetric octagon of any size by rhombi. This result uses the Gessel-Viennot technique and generalizes to any octagon a formula given by Elnitsky in a special case.
Publié le : 2004-07-05
Classification:
random tilings,
enumeration,
entropy,
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
@article{hal-00123850,
author = {Destainville, Nicolas and Mosseri, R. and Bailly, F.},
title = {A formula for the number of tilings of an octagon by rhombi},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00123850}
}
Destainville, Nicolas; Mosseri, R.; Bailly, F. A formula for the number of tilings of an octagon by rhombi. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00123850/