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On the Problem of Molluzzo for the Modulus 4

Jonathan Chappelon / Shalom Eliahou
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2012-0001

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Abstract.

We solve the currently smallest open case in the 1976 problem of Molluzzo on , namely the case . This amounts to constructing, for all positive integers n congruent to 0 or 7 mod 8, a sequence of integers modulo 4 of length n generating, by Pascal's rule, a Steinhaus triangle containing 0, 1, 2, 3 with equal multiplicities.

Keywords: Molluzzo's Problem; Steinhaus Triangles; Balanced Triangles; Multisets; Pascal's Rule

About the article

Received: 2011-05-05

Revised: 2011-12-18

Accepted: 2012-02-16

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 723–739, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2012-0001.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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