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Licensed Unlicensed Requires Authentication Published by De Gruyter September 9, 2010

Subsets of ℤ with Simultaneous Orderings

David Adam , Jean-Luc Chabert and Youssef Fares
From the journal


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.

Received: 2010-01-28
Revised: 2010-04-21
Accepted: 2010-04-28
Published Online: 2010-09-09
Published in Print: 2010-September

© de Gruyter 2010

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