# The Postage Stamp Problem and Its Applications

 dc.contributor.advisor Jia, Xingde dc.contributor.author Song, Zhaochen dc.contributor.committeeMember Keller, Thomas M. dc.contributor.committeeMember Gu, Weizhen dc.date.accessioned 2024-01-03T23:34:28Z dc.date.available 2024-01-03T23:34:28Z dc.date.issued 2014-05 dc.description.abstract Let A = { 0 = a0 < a1 < a2 < · · · < ak} be a set of k + l nonnegative integers. Let n(h, A) denote the largest positive integer n so that every integer x E [O, n] can be written as a sum of exactly h not necessarily distinct elements from A, where [a, b] denotes the set of integers x : a ~ :r; :s; b. Let k be a positive integers. Define n(h, k) = max{n(h, A) I AC N and IAI = k + 1}, where N is the set of all nonnegative integers. Using the definition of n(h, A), we can further rewrite n(h, k) as n(h, k) = max{n I AC N, IAi = k + 1, and hA ~ [O, n]}. The postage stamp problem is the study of n(h, k) and other related problems. In this thesis, we mainly focus on postage stamp problem and some extremal bases for finite cyclic groups, a closely related problem with applications in information network design. We will introduce some extremal functions, namely n(h, 2) and n(h, 3), and discuss some simple properties and estimates of them. This will further expand to the discussion of some other bases and extremal functions with lager k or n values. Some other closely related problem, such as the extremal bases for finite cyclic groups and the Frobenius coin problem, will also be studied in this thesis. dc.description.department Mathematics dc.format Text dc.format.extent 76 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Song, Z. (2014). The postage stamp problem and its applications (Unpublished thesis). Texas State University, San Marcos, Texas. dc.identifier.uri https://hdl.handle.net/10877/17895 dc.language.iso en dc.subject number theory dc.subject additive functions dc.subject finite groups dc.title The Postage Stamp Problem and Its Applications dc.type Thesis thesis.degree.department Mathematics thesis.degree.discipline Mathematics thesis.degree.grantor Texas State University thesis.degree.level Masters thesis.degree.name Master of Science

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