Related papers: Binary words avoiding xx^Rx and strongly unimodal …
We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings,…
In 2005, Rampersad and the second author proved a number of theorems about infinite words x with the property that if w is any sufficiently long finite factor of x, then its reversal w^R is not a factor of x. In this note we revisit these…
We investigate the avoidability of unary patterns of size of four with morphic permutations. More precisely, we show that, for the positive integers $i,j,k$, the sizes of the alphabets over which a pattern $x \pi ^ {i} (x) \pi^{j}(x)…
Permutations avoiding all patterns of a given shape (in the sense of Robinson-Schensted-Knuth) are considered. We show that the shapes of all such permutations are contained in a suitable thick hook, and deduce an exponential growth rate…
Good words are binary words avoiding factors 11 and 1001, and patterns 0000 and 00010100. We show that good words bear the same relationship to the period-doubling sequence that overlap-free words bear to the Thue-Morse sequence. We prove…
In this paper, we consider two sets of pattern-avoiding ascent sequences: those avoiding both 201 and 210 and those avoiding 0021. In each case we show that the number of such ascent sequences is given by the binomial convolution of the…
The class of permutations that avoid the bivincular pattern (231, {1},{1}) is known to be enumerated by the Fishburn numbers. In this paper, we call them Fishburn permutations and study their pattern avoidance. For classical patterns of…
The number of 123-avoiding permutation on $\{1,2,\ldots,n\}$ with a fixed leading terms is counted by the ballot numbers. The same holds for $132$-avoiding permutations. These results were proved by Miner and Pak using the…
We study words that barely avoid repetitions, for several senses of "barely". A squarefree (respectively, overlap-free, cubefree) word is irreducible if removing any one of its interior letters creates a square (respectively, overlap,…
In [BabStein] Babson and Steingr\'{\i}msson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. In [Kit1] Kitaev considered simultaneous…
The purpose of this paper is to investigate the connection between context-free grammars and normal ordering problem, and then to explore various extensions of the Stirling grammar. We present grammatical characterizations of several well…
We use results on Dyck words and lattice paths to derive a formula for the exact number of binary words of a given length with a given minimal abelian border length, tightening a bound on that number from Christodoulakis et al. (Discrete…
How long can a word be that avoids the unavoidable? Word $W$ encounters word $V$ provided there is a homomorphism $\phi$ defined by mapping letters to nonempty words such that $\phi(V)$ is a subword of $W$. Otherwise, $W$ is said to avoid…
The set of all avoidable patterns in n or fewer letters can be avoided on an alphabet with 2(n+2) letters.
We completely characterize the words that can be avoided in infinite squarefree ternary words.
We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. We concentrate on fractional exponents of finite words and…
In a recent paper, Bona and Smith define the notion of \textit{strong avoidance}, in which a permutation and its square both avoid a given pattern. In this paper, we generalize this idea to what we call \textit{chain avoidance}. We say that…
Taking a combinatorial point of view on cyclotomic polynomials leads to a larger class of polynomials we shall call the inclusion-exclusion polynomials. This gives a more appropriate setting for certain types of questions about the…
Recently, Babson and Steingrimsson have introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider pattern avoidance for such patterns, and…
Finding statistically significant interactions between binary variables is computationally and statistically challenging in high-dimensional settings, due to the combinatorial explosion in the number of hypotheses. Terada et al. recently…