✦ LIBER ✦

Domino tilings of rectangles with fixed width

✍ Scribed by David Klarner; Jordan Pollack

Publisher: Elsevier Science
Year: 1980
Tongue: English
Weight: 761 KB
Volume: 32
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90098-9

No coin nor oath required. For personal study only.

✦ Synopsis

Let t(k, n) denote the number of ways to tile a C x n rectangle with 1 x 2 rectangles (called dominoes). We show that for each fixed k the s( quence tk = (t(k, O), t(k, I), . . .) satisfies a difference equation (linear, homogeneous, and w ith constant coefficients). Furthermore, a computational method is given for finding this di Terence equation together with the initial terms of the sequence. This gives rise to a new way to compute t(k, n) which differs completely with the known Pfaffian method. The generating fr nction of r, is a rational function Fk, and Fk is given explicitly for k = 1,. . . ,8. We end w+_i r ,ome conjectures concerning the form of Fk based on our computations.

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