Related papers: Subword enumeration up to stack-sorting equivalenc…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
We consider a generalized Riemann-Hurwitz formula as it may be applied to rational maps between projective varieties having an indeterminacy set and fold-like singularities. The case of a holomorphic branched covering map is recalled. Then…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
In this paper we investigate local to global phenomena for a new family of complexity functions of infinite words indexed by $k \in \Ni \cup \{+\infty\}$ where $\Ni$ denotes the set of positive integers. Two finite words $u$ and $v$ in…
We combine the language of monoids with the language of preorders so as to refine some fundamental aspects of the classical theory of factorization and prove an abstract factorization theorem with a variety of applications. In particular,…
We study a binary Thue--Morse-type sequence arising from the base-$3/2$ expansion of integers, an archetypal automatic sequence in a rational base numeration system. Because the sequence is generated by a periodic iteration of morphisms…
The sort transform (ST) is a modification of the Burrows-Wheeler transform (BWT). Both transformations map an arbitrary word of length n to a pair consisting of a word of length n and an index between 1 and n. The BWT sorts all rotation…
A subset $A$ of $\mathbb{N}$ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $(x_n)_{n\in \mathbb{N}} $ of natural numbers. Central sets, first introduced by Furstenberg using notions from…
On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates the description and computation via Morse theory of key topological invariants. Here we establish checkable…
In the study of infinite words, various notions of balancedness provide quantitative measures for how regularly letters or factors occur, and they find applications in several areas of mathematics and theoretical computer science. In this…
Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and T: X --> X is the…
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…
We study a class of infinite words $x_k$ , where $k$ is a positive integer, recently introduced by J. Shallit. This class includes the Thue-Morse sequence $x_1$, the Fibonacci-Thue-Morse sequence $x_2$, and the Allouche-Johnson sequence…
Let $s$ be West's stack-sorting map, and let $s_{T}$ be the generalized stack-sorting map, where instead of being required to increase, the stack avoids subpermutations that are order-isomorphic to any permutation in the set $T$. In 2020,…
This manuscript recounts some of the author's contributions to algebraic and enumerative combinatorics. We have focused on two types of generalizations of bipartite maps, which are bipartite graphs embedded on surfaces. Maps are known to…
We define the Thue-Morse transform T on a class of infinite binary words. It sends the alternating word a_0 = 010101... to the Thue-Morse sequence. We then study its orbit a_m = T^m(a_0) as well as the sequences u_m and v_m giving…
Despite having been introduced in 1962 by C.L. Mallows, the combinatorial algorithm Patience Sorting is only now beginning to receive significant attention due to such recent deep results as the Baik-Deift-Johansson Theorem that connect it…
We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that -- the Thue-Morse word has the minimum possible subword complexity over all overlap-free…
Constellations and hypermaps generalize combinatorial maps, i.e. embedding of graphs in a surface, in terms of factorization of permutations. In this paper, we extend a result of Jackson and Visentin (1990) stating an enumerative relation…
The positive effect of adding subword information to word embeddings has been demonstrated for predictive models. In this paper we investigate whether similar benefits can also be derived from incorporating subwords into counting models. We…