Words avoiding reversed subwords

计数不含固定长度严格递增子词的单词

Counting words without strictly increasing subwords of fixed length

本文推导了计数不含长度为k的严格递增子词的n元单词数量的生成函数精确公式，并给出其应用。

计算不含固定长度非递减子词的单词数量

Counting words without non-decreasing subwords of fixed length

本文研究计算不含固定长度非递减子词的单词数量问题，先在arXiv:2511.13287中得出相关生成函数精确公式及应用等，还猜测了其他公式，本文对这些猜测公式进行了证明。

Words Avoiding Reversed Factors, Revisited

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 results, reproving them in more generality, using machine computations only. Two different techniques are presented.

On Simsun and Double Simsun Permutations Avoiding a Pattern of Length Three

A permutation $σ\in\mathfrak{S}_n$ is simsun if for all $k$, the subword of $σ$ restricted to $\{1,...,k\}$ does not have three consecutive decreasing elements. The permutation $σ$ is double simsun if both $σ$ and $σ^{-1}$ are simsun. In this paper we present a new bijection between simsun permutations and increasing 1-2 trees, and show a number of interesting consequences of this bijection in the enumeration of pattern-avoiding simsun and double simsun permutations. We also enumerate the double simsun permutations that avoid each pattern of length three.

Avoiding 2-binomial squares and cubes

Two finite words $u,v$ are 2-binomially equivalent if, for all words $x$ of length at most 2, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word $uv$ where $u$ and $v$ are 2-binomially equivalent. In this paper, considering pure morphic words, we prove that 2-binomial squares (resp. cubes) are avoidable over a 3-letter (resp. 2-letter) alphabet. The sizes of the alphabets are optimal.

Representing Graphs via Pattern Avoiding Words

The notion of a word-representable graph has been studied in a series of papers in the literature. A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy$ is an edge in $E$. If $V =\{1, \ldots, n\}$, this is equivalent to saying that $G$ is word-representable if for all $x,y \in \{1, \ldots, n\}$, $xy \in E$ if and only if the subword $w_{\{x,y\}}$ of $w$ consisting of all occurrences of $x$ or $y$ in $w$ has no consecutive occurrence of the pattern 11. In this paper, we introduce the study of $…