Tromino tilings of Domino-Deficient Rectangles
| dc.creator | Aanjaneya, Mridul | |
| dc.date | 2006-06-13 | |
| dc.date | 2007-08-13 | |
| dc.date.accessioned | 2026-07-07T08:23:13Z | |
| dc.date.available | 2026-07-07T08:23:13Z | |
| dc.description | We consider tromino tilings of $m\times n$ domino-deficient rectangles, where $3|(mn-2)$ and $m,n\geq0$, and characterize all cases of domino removal that admit such tilings, thereby settling the open problem posed by J. M. Ash and S. Golomb in \cite {marshall}. Based on this characterization, we design a procedure for constructing such a tiling if one exists. We also consider the problem of counting such tilings and derive the exact formula for the number of tilings for $2\times(3t+1)$ rectangles, the exact generating function for $4\times(3t+2)$ rectangles, where $t\geq0$, and an upper bound on the number of tromino tilings for $m\times n$ domino-deficient rectangles. We also consider general 2-deficiency in $n\times4$ rectangles, where $n\geq8$, and characterize all pairs of squares which do not permit a tromino tiling. | |
| dc.description | 19 pages, 13 figures | |
| dc.identifier | https://arxiv.org/abs/cs/0606059 | |
| dc.identifier | http://arxiv.org/abs/cs/0606059 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135916 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Combinatorics | |
| dc.title | Tromino tilings of Domino-Deficient Rectangles | |
| dc.type | text |