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Subsets of ℤ with Simultaneous Orderings

David Adam
  • Université de la Polynésie Française, BP 6570, 98702 Faa'a, Tahiti, French Polynesia. E-mail:
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/ Jean-Luc Chabert / Youssef Fares
Published Online: 2010-09-09 | DOI: https://doi.org/10.1515/integ.2010.037


We are interested in subsets S of ℤ which admit simultaneous orderings, that is, sequences {an }n≥0 such that divides for every xS (analogously to n! which divides (m + n)!/m! for every m). In particular, we characterize the polynomials ƒ of degree 2 such that ƒ(ℕ) admits a simultaneous ordering.

Keywords.: Simultaneous orderings; factorials; integer-valued polynomials

About the article

Received: 2010-01-28

Revised: 2010-04-21

Accepted: 2010-04-28

Published Online: 2010-09-09

Published in Print: 2010-09-01

Citation Information: Integers, Volume 10, Issue 4, Pages 437–451, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2010.037.

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