The domino tilings of Aztec rectangles with holes and the Gauss hypergeometric series
par
Masao Ishikawa(Université d'Okayama)
→
Europe/Paris
Salle Fokko du Cloux (ICJ)
Salle Fokko du Cloux
ICJ
1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
Description
We study the number of domino tilings of an
Aztec rectangle with even number of consecutive holes in a line
and we obtain a formula which express the number of such domino
tilings by a product of a power of 2, a nice product and a
polynomial of the coordinates of the holes. We will find a
formula which expresses this polynomial as a determinant of
terminating Gauss hypergeometric series. First we use the
Lindstrom-Gessel-Viennot theorem to enumerate the domino
tilings of an Aztec rectangle with consecutive holes and obtain a
determinant whose entries are generalized large Schroder numbers.
