Journal of Integer Sequences, Vol. 17 (2014), Article 14.5.5

Combinatorial Proofs of Some Formulas for Triangular Tilings

Mark Shattuck
Department of Mathematics
University of Tennessee
Knoxville, TN 37996


Bodeen et al. recently considered a new combinatorial tiling problem wherein a "strip" is tiled using triangles of four types and derived various identities for the resulting numbers. Some of the identities were proven combinatorially and others only algebraically, and the question of finding combinatorial interpretations of all of their results was posed. In this note, we provide the requested bijective proofs. To do so, we rephrase the question in an equivalent form in terms of tiling a strip with squares, trominos, and three types of dominos and form bijections or near bijections where the cardinality of various size families of sets gives the correct result.

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(Concerned with sequences A000045 A000129 A097076.)

Received January 19 2014; revised version received March 20 2014. Published in Journal of Integer Sequences, March 24 2014.

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