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Reznick, Bruce A. Hildebrand, A.J. Boca, Florin Reznick, Bruce A. Ahlgren, Scott Tangjai, Wipawee 2014-09-16T17:26:10Z 2014-09-16T17:26:10Z 2014-08 2014-09-16 2014-08 In this dissertation, we study a family of non-standard digital representations in base 3. Let A be an index set such that A={0,u1,u2}, where u1 is equivalent to 1 (mod 3) and u2 is equivalent to 2 (mod 3). We study the set of integers which can be written as \sum_{i=0}^{\infty}\epsilon_i 3^i, where \epsilon_i is in A. Most of the work in this dissertation is about the case that the index set A={0,1,5}. We are particularly interested in the maximal sets of consecutive integers, the density of the represented numbers and the related generating functions. Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-05-09T13:35:32Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Tangjai_Wipawee.pdf: 26104090 bytes, checksum: 976099e6ad1ac471cdd51c19c76055c5 (MD5) Made available in DSpace on 2014-09-16T17:26:10Z (GMT). No. of bitstreams: 2 Wipawee_Tangjai.pdf: 26095425 bytes, checksum: e9ba0d9638a506cc52439465d5235f89 (MD5) license.txt: 4065 bytes, checksum: f0b8c83f0b36ed39fb027bf29df9d428 (MD5) http://hdl.handle.net/2142/50750 en Copyright 2014 Wipawee Tangjai Combinatorial number theory Digital representation non-standard digit sets ternary representations generating functions sequences subsets of integers Density and spacing properties of some families of non-standard ternary representations text 1257 Mathematics Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD