Combinatorial Proofs of Some Formulas for Triangular Tilings
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.
Full version: pdf,
(Concerned with sequences
Received January 19 2014;
revised version received March 20 2014.
Published in Journal of Integer Sequences, March 24 2014.
Journal of Integer Sequences home page