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Automatic counting of tilings of skinny plane regions. (English) Zbl 1302.05032

Blackburn, Simon R. (ed.) et al., Surveys in combinatorics 2013. Papers based on the 24th British combinatorial conference, London, UK, June 30 – July 5, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-65195-1/pbk; 978-1-139-50674-8/ebook). London Mathematical Society Lecture Note Series 409, 363-378 (2013).
The paper deals with counting the number of tilings of some plane regions. The authors were inspired by a problem proposed by D. Knuth. The results are proved by an inductive method using \(C\)-finite sequences.
The article is accompanied with Maple packages. In particular, they count the number of domino tilings of a rectangle, of a holey rectangle, of a cross.
For the entire collection see [Zbl 1286.05002].

MSC:

05B45 Combinatorial aspects of tessellation and tiling problems
05A15 Exact enumeration problems, generating functions

Software:

RITSUF; TILINGS; Maple
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