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We propose a new ternary infinite (even full-infinite) square-free sequence. The sequence is defined both by an iterative method and by a direct definition. Both definitions are analogous to those of the Thue-Morse sequence. The direct definition is given by a deterministic finite automaton with output. In short, the sequence is automatic.
Partly in service of exploring the formal basis for Georgetown Universitys AvesTerra database structure, we formalize a recursive hypergraph data structure, which we call an ubergraph.
Distance-preserving mappings (DPMs) are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of the same or longer length such that every two distinct vectors are mapped to permutations with the same or even larger
Let $S_{N}(P)$ be the poset obtained by adding a dummy vertex on each diagonal edge of the $N$s of a finite poset $P$. We show that $S_{N}(S_{N}(P))$ is $N$-free. It follows that this poset is the smallest $N$-free barycentric subdivision of the diag
We consider a search problem on a $2$-dimensional infinite grid with a single mobile agent. The goal of the agent is to find her way home, which is located in a grid cell chosen by an adversary. Initially, the agent is provided with an infinite seque
This contribution is devoted to the study of positional numeration systems with negative base introduced by Ito and Sadahiro in 2009, called (-beta)-expansions. We give an admissibility criterion for more general case of (-beta)-expansions and discus