Pachter, Lior (1997) Combinatorial Approaches and Conjectures for 2-Divisibility Problems Concerning Domino Tilings of Polyominoes. Electronic Journal of Combinatorics, 4 (1). Art. No. R29. ISSN 1077-8926. https://resolver.caltech.edu/CaltechAUTHORS:20170309-144854496
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Abstract
We give the first complete combinatorial proof of the fact that the number of domino tilings of the 2n×2n square grid is of the form 2^n(2k + 1)^2, thus settling a question raised by John, Sachs, and Zernitz. The proof lends itself naturally to some interesting generalizations, and leads to a number of new conjectures.
| Item Type: | Article | ||||||
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| Additional Information: | © 1997 The Author. Submitted: September 24, 1997; Accepted: November 8, 1997. We thank Joshua Bao and Jim Propp for helpful suggestions and comments. Special thanks go to Glenn Tesler for helping to draw the tiling pictures and to David Wilson for providing his program vax.el with which all the conjectures were tested. Finally, we are indebted to the anonymous referee for excellent suggestions which greatly helped in improving the final version of the paper. | ||||||
| Issue or Number: | 1 | ||||||
| Classification Code: | Mathematical Subject Classification: Primary 05C7 | ||||||
| Record Number: | CaltechAUTHORS:20170309-144854496 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170309-144854496 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 75001 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | George Porter | ||||||
| Deposited On: | 13 Mar 2017 16:10 | ||||||
| Last Modified: | 24 Feb 2020 10:30 |
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