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Our goal in this article is to review the known properties of the mysterious Kolakoski sequence and at the same time look at generalizations of it over arbitrary two letter alphabets. Our primary focus will here be the case where one of the letters is odd while the other is even, since in the other cases the sequences in question can be rewritten as (well-known) primitive substitution sequences. We will look at word and letter frequencies, squares, palindromes and complexity.
Given a set of integers with no three in arithmetic progression, we construct a Stanley sequence by adding integers greedily so that no arithmetic progression is formed. This paper offers two main contributions to the theory of Stanley sequences. Fir
Given a set of integers containing no 3-term arithmetic progressions, one constructs a Stanley sequence by choosing integers greedily without forming such a progression. Independent Stanley sequences are a well-structured class of Stanley sequences w
We study pairs of graphs (H_1,H_2) such that every graph with the densities of H_1 and H_2 close to the densities of H_1 and H_2 in a random graph is quasirandom; such pairs (H_1,H_2) are called forcing. Non-bipartite forcing pairs were first discove
In this paper we demonstrate connections between three seemingly unrelated concepts. (1) The discrete isoperimetric problem in the infinite binary tree with all the leaves at the same level, $ {mathcal T}_{infty}$: The $n$-th edge isoperimetric n
Let $pi_1=(d_1^{(1)}, ldots,d_n^{(1)})$ and $pi_2=(d_1^{(2)},ldots,d_n^{(2)})$ be graphic sequences. We say they emph{pack} if there exist edge-disjoint realizations $G_1$ and $G_2$ of $pi_1$ and $pi_2$, respectively, on vertex set ${v_1,dots,v_n}$ s