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Bounds on degrees of p-adic separating polynomials

Katz, Daniel J. and Zahl, Joshua (2008) Bounds on degrees of p-adic separating polynomials. Journal of Combinatorial Theory. Series A, 115 (7). pp. 1310-1319. ISSN 0097-3165. doi:10.1016/j.jcta.2008.01.007.

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We study a discrete optimization problem introduced by Babai, Frankl, Kutin, and Stefankovic (2001), which provides bounds on degrees of polynomials with p-adically controlled behavior. Such polynomials are of particular interest because they furnish bounds on the size of set systems satisfying Frankl-Wilson-type conditions modulo prime powers, with lower degree polynomials providing better bounds. We elucidate the asymptotic structure of solutions to the optimization problem, and we also provide an improved method for finding solutions in certain circumstances.

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Additional Information:© 2008 Elsevier Inc. Received 18 July 2007. Available online 17 March 2008. Communicated by Bruce Rothschild. The authors wish to thank Richard M. Wilson for his helpful advice on this work and its presentation.
Subject Keywords:separating polynomials; restricted intersections modulo prime powers; extremal set theory
Issue or Number:7
Record Number:CaltechAUTHORS:KATjcta08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13581
Deposited By: Tony Diaz
Deposited On:08 May 2009 18:45
Last Modified:08 Nov 2021 22:39

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