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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

A Tiling Approach to Chebyshev Polynomials

Walton, Daniel 01 May 2007 (has links)
We present a combinatorial interpretation of Chebyshev polynomials. The nth Chebyshev polynomial of the first kind, Tn(x), counts the sum of all weights of n-tilings using light and dark squares of weight x and dominoes of weight −1, and the first tile, if a square must be light. If we relax the condition that the first square must be light, the sum of all weights is the nth Chebyshev polynomial of the second kind, Un(x). In this paper we prove many of the beautiful Chebyshev identities using the tiling interpretation.

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