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Van der Waerden's Theorem and Avoidability in Words
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Yu-Hin Au
,
Aaron Robertson
Published/Copyright:
February 24, 2011
Abstract
Independently, Pirillo and Varricchio, Halbeisen and Hungerbühler and Freedman considered the following problem, open since 1992: Does there exist an infinite word w over a finite subset of ℤ such that w contains no two consecutive blocks of the same length and sum? We consider some variations on this problem in the light of van der Waerden's theorem on arithmetic progressions.
Received: 2010-08-03
Revised: 2010-11-11
Accepted: 2010-11-26
Published Online: 2011-02-24
Published in Print: 2011-February
© de Gruyter 2011
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Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
