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Two Theorems about Similarity Maps
Andreas Dress1,2, Tatjana Lokot3, Walter Schubert4 and Peter Serocka1,2
1CAS-MPG Partner Institute for Computational Biology, 320 Yue Yang Road, Shanghai 200031, P.R. China
2Max-Planck-Institut f\"ur Mathematik in den Naturwissenschaften, Inselstrasse 2-26 D-04103 Leipzig, Germany
{andreas, pserocka}@picb.ac.cn
3Fakul\"at f\"ur Mathematik, Universit\"at Bielefeld, D-33615 Bielefeld, Germany
tlokot@mathematik.uni-bielefeld.de
4Institut of Medical Neurobiology, University of Magdeburg, D-39120 Magdeburg, Germany
Walter.Schubert@med.ovgu.de
Annals of Combinatorics 12 (3) pp.279-290 September, 2008
AMS Subject Classification: 05A19
Abstract:
In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities.
Keywords: Pell numbers, combinatorial identities, tilings, NSW numbers

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