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We characterize the squares occurring in infinite overlap-free binary words and construct various power-free binary words containing infinitely many overlaps.
We prove that the minimum number of distinct hamiltonian paths in a strong tournament of order n is 5 n-1 3 . A known construction shows this number is best possible when n 1 mod...
Let T be the Cayley graph of a finitely generated free group F. Given two vertices in T consider all the walks of a given length between these vertices that at a certain time must...
In the game of Penney Ante two players take turns publicly selecting two distinct words of length n using letters from an alphabet of size q. They roll a fair q sided die having ...
The reduced canonical form of a loopfree game G is the simplest game infinitesimally close to G. Reduced canonical forms were introduced by Calistrate, and Grossman and Siegel pro...
Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square or...