相关论文: Ternary is Still Good for Parikh Matrices
Ternary paths consist of an up-step of one unit, a down-step of two units, never go below the $x$-axis, and return to the $x$-axis. This paper addresses the enumeration of partial ternary paths, ending at a given level $i$, reading the path…
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
We describe witness languages meeting the upper bound on the state complexity of the multiple concatenation of $k$ regular languages over an alphabet of size $k+1$ with a significantly simpler proof than that in the literature. We also…
We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…
Three types of the Parikh mapping are introduced, namely, alphabetic, alphabetic-basis and basis. Explicit expressions for attractors of the k-th order in bases n >= 8, including countable ones, are found. Properties for the alphabetic,…
Two words are $k$-binomially equivalent if each subword of length at most $k$ occurs the same number of times in both words. The $k$-binomial complexity of an infinite word is a counting function that maps $n$ to the number of $k$-binomial…
Circular words are cyclically ordered finite sequences of letters. We give a computer-free proof of the following result by Currie: square-free circular words over the ternary alphabet exist for all lengths $l$ except for 5, 7, 9, 10, 14,…
One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete…
We aim at enforcing hard constraints to impose a global structure on sequences generated from Markov models. In this report, we study the complexity of sampling Markov sequences under two classes of constraints: Binary Equalities and…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
In light of recent hardware advances, it is striking that real arithmetic in balanced ternary logic has received almost no attention in the literature. This is particularly surprising given ternary logic's promising properties, which could…
Recently, a new characterization of Lyndon words that are also perfectly clustering was proposed by Lapointe and Reutenauer (2024). A word over a ternary alphabet {a,b,c} is called perfectly clustering Lyndon if and only if it is the…
In 1991 H\'ebrard introduced a factorization of words that turned out to be a powerful tool for the investigation of a word's scattered factors (also known as (scattered) subwords or subsequences). Based on this, first Karandikar and…
The family, L(INDLIN), of languages generated by linear indexed grammars has been studied in the literature. It is known that the Parikh image of every language in L(INDLIN) is semi-linear. However, there are bounded semi linear languages…
In the past few years, the slice-rank lemma of Tao has been applied successfully to many problems in extremal combinatorics. In this paper, first, we define a new notion of triangular tensors which generalizes that of triangular matrices…
Various variants of Parikh automata on infinite words have recently been introduced in the literature. However, with some exceptions only their non-deterministic versions have been considered. In this paper we study the deterministic…
Cyclic equalizability is a notion introduced by Shinagawa and Nuida in 2025, in the study of card-based cryptography. Informally, a collection of words is cyclically equalizable if, by inserting the same letters at the same positions in all…
We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to…
We argue that predicate languages and their Tarskian structures have an important place for the study of concurrency. The argument in our paper is based on an example: we show that two seemingly dissimilar algorithms have a common set of…