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On the Problem of Molluzzo for the Modulus 4

  • Jonathan Chappelon EMAIL logo and Shalom Eliahou
Published/Copyright: August 1, 2012
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Integers
From the journal Integers Volume 12 Issue 4

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
Received: 2011-05-05
Revised: 2011-12-18
Accepted: 2012-02-16
Published Online: 2012-08-01
Published in Print: 2012-08-01

© 2012 by Walter de Gruyter Berlin Boston

Articles in the same Issue

  1. Masthead
  2. On Weakly Complete Sequences Formed by the Greedy Algorithm
  3. Bijective Proofs of Vajda's Ninetieth Fibonacci Number Identity and Related Identities
  4. Newman Polynomials, Reducibility, and Roots on the Unit Circle
  5. A Property of Twin Primes
  6. Number of Permutations with Prescribed Up-Down Structure as a Function of Two Variables
  7. A -Expansion Associated to Sturmian Sequences
  8. On the Number of Carries Occurring in an Addition Mod 
  9. A Probabilistic Look at Series Involving Euler's Totient Function
  10. Fibonacci Variations of a Conjecture of Polignac
  11. Extending Nathanson Heights to Arbitrary Finite Fields
  12. On the Maximal Cross Number of Unique Factorization Zero-Sum Sequences over a Finite Abelian Group
  13. An Explicit Bound for Aliquot Cycles of Repdigits
  14. A Note on the Minimal Number of Representations in 
  15. A Unified Proof of Two Classical Theorems on CNS Polynomials
  16. On the Problem of Molluzzo for the Modulus 4
  17. On Multiplicative Functions with Bounded Partial Sums
  18. Avoiding Type or Patterns in a Partition of a Set
https://doi.org/10.1515/integers-2012-0001
Keywords for this article
Molluzzo's Problem; Steinhaus Triangles; Balanced Triangles; Multisets; Pascal's Rule

Articles in the same Issue

  1. Masthead
  2. On Weakly Complete Sequences Formed by the Greedy Algorithm
  3. Bijective Proofs of Vajda's Ninetieth Fibonacci Number Identity and Related Identities
  4. Newman Polynomials, Reducibility, and Roots on the Unit Circle
  5. A Property of Twin Primes
  6. Number of Permutations with Prescribed Up-Down Structure as a Function of Two Variables
  7. A -Expansion Associated to Sturmian Sequences
  8. On the Number of Carries Occurring in an Addition Mod 
  9. A Probabilistic Look at Series Involving Euler's Totient Function
  10. Fibonacci Variations of a Conjecture of Polignac
  11. Extending Nathanson Heights to Arbitrary Finite Fields
  12. On the Maximal Cross Number of Unique Factorization Zero-Sum Sequences over a Finite Abelian Group
  13. An Explicit Bound for Aliquot Cycles of Repdigits
  14. A Note on the Minimal Number of Representations in 
  15. A Unified Proof of Two Classical Theorems on CNS Polynomials
  16. On the Problem of Molluzzo for the Modulus 4
  17. On Multiplicative Functions with Bounded Partial Sums
  18. Avoiding Type or Patterns in a Partition of a Set
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