Newman polynomials with prescribed vanishing and integer sets with distinct subset sums
Authors:
Peter Borwein and Michael J. Mossinghoff
Journal:
Math. Comp. 72 (2003), 787800
MSC (2000):
Primary 11C08, 11B75, 11P99; Secondary :, 05D99, 11Y55
Published electronically:
July 15, 2002
MathSciNet review:
1954968
Fulltext PDF Free Access
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Abstract: We study the problem of determining the minimal degree of a polynomial that has all coefficients in and a zero of multiplicity at . We show that a greedy solution is optimal precisely when , mirroring a result of Boyd on polynomials with coefficients. We then examine polynomials of the form , where is a set of positive odd integers with distinct subset sums, and we develop algorithms to determine the minimal degree of such a polynomial. We determine that satisfies inequalities of the form . Last, we consider the related problem of finding a set of positive integers with distinct subset sums and minimal largest element and show that the ConwayGuy sequence yields the optimal solution for , extending some computations of Lunnon.
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Additional Information
Peter Borwein
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email:
pborwein@cecm.sfu.ca
Michael J. Mossinghoff
Affiliation:
Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095
Email:
mjm@math.ucla.edu
DOI:
http://dx.doi.org/10.1090/S0025571802014606
PII:
S 00255718(02)014606
Keywords:
Newman polynomial; pure product; sumdistinct sets; ConwayGuy sequence
Received by editor(s):
July 23, 2001
Published electronically:
July 15, 2002
Article copyright:
© Copyright 2002 American Mathematical Society
