A reciprocity theorem for domino tilings
| dc.creator | Propp, James | |
| dc.date | 2001-04-01 | |
| dc.date.accessioned | 2026-07-07T04:40:55Z | |
| dc.date.available | 2026-07-07T04:40:55Z | |
| dc.description | Let T(m,n) denote the number of ways to tile an m-by-n rectangle with dominos. For any fixed m, the numbers T(m,n) satisfy a linear recurrence relation, and so may be extrapolated to negative values of n; these extrapolated values satisfy the relation T(m,-2-n) = epsilon_{m,n} T(m,n), where epsilon_{m,n} is -1 if m is congruent to 2 (mod 4) and n is odd, and is +1 is otherwise. This is equivalent to a fact demonstrated by Stanley using algebraic methods. Here I give a proof that provides, among other things, a uniform combinatorial interpretation of T(m,n) that applies regardless of the sign of n. | |
| dc.description | 5 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0104011 | |
| dc.identifier | http://arxiv.org/abs/math/0104011 | |
| dc.identifier | Electron. J. Combin. 8, no. 1, Research Paper 18 (2001). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61203 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 | |
| dc.title | A reciprocity theorem for domino tilings | |
| dc.type | text |