Related papers: Rationality, irrationality, and Wilf equivalence i…
To a word $w$, we associate the rational function $\Psi_w = \prod (x_{w_i} - x_{w_{i+1}})^{-1}$. The main object, introduced by C. Greene to generalize identities linked to Murnaghan-Nakayama rule, is a sum of its images by certain…
In this paper we define Ordered Generating System for finite non-abelian groups, which is a generalization of the basis theorem for finite abelian groups. We prove the following: If each composition factor of a group G has Ordered…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
A finite group $G$ is called $k$-factorizable if for every ordered factorization $|G|=a_1\cdots a_k$ into integers each greater than $1$ there exist subsets $A_1,\dots,A_k\subseteq G$ such that $|A_i|=a_i$ for each $i$ and $G=A_1\cdots…
Given a finite poset $P$, we associate a simple graph denoted by $G_P$ with all connected order ideals of $P$ as vertices, and two vertices are adjacent if and only if they have nonempty intersection and are incomparable with respect to set…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
Schm\"udgen's Theorem says that if a basic closed semialgebraic set K = {g_1 \geq 0, ..., g_s \geq 0} in R^n is compact, then any polynomial f which is strictly positive on K is in the preordering generated by the g_i's. Putinar's Theorem…
Let $P\in\mathbb{P}_1(\mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $\mathbb{Z}$. With elementary techniques one sees that the minimal periodicity of $P$ is at most $2$. Recently we proved a generalization of…
A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u=v. Suffix-, factor-, and subword-free languages are defined similarly, where "subword" means "subsequence". A language is bifix-free if it is…
We continue the study of separable elements in finite Weyl groups. These elements generalize the well-studied class of separable permutations. We show that the multiplication map $W/U \times U \to W$ is a length-additive bijection, or…
As highlighted in a series of recent papers by Tringali and the author, fundamental aspects of the classical theory of factorization can be significantly generalized by blending the languages of monoids and preorders. Specifically, the…
We consider the task of weighted first-order model counting (WFOMC) used for probabilistic inference in the area of statistical relational learning. Given a formula $\phi$, domain size $n$ and a pair of weight functions, what is the…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…
Given a (finite or infinite) subset $X$ of the free monoid $A^*$ over a finite alphabet $A$, the rank of $X$ is the minimal cardinality of a set $F$ such that $X \subseteq F^*$. A submonoid $M$ generated by $k$ elements of $A^*$ is…
The binomial notation (w u) represents the number of occurrences of the word u as a (scattered) subword in w. We first introduce and study possible uses of a geometrical interpretation of (w ab) and (w ba) when a and b are distinct letters.…
In this paper, we study an abelian-type property of infinite words called well distributed occurrences, or WELLDOC for short. An infinite word $w$ on a $d$-ary alphabet has the WELLDOC property if, for each factor $u$ of $w$, positive…
Let $f$ be a measurable, real function defined in a neighbourhood of infinity. The function $f$ is said to be of generalised regular variation if there exist functions $h \not\equiv 0$ and $g > 0$ such that $f(xt) - f(t) = h(x) g(t) +…
An element w in the free group on r letters defines a map f from G^r to G for each group G. In this note, we show that whenever w is non-trivial and G is a semisimple algebraic group, f is dominant. When G is a finite simple group, the…
A finite word u is said to be bordered if u has a proper prefix which is also a suffix of u, and unbordered otherwise. Ehrenfeucht and Silberger proved that an infinite word is purely periodic if and only if it contains only finitely many…
Given a word $w$ over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which $w$ occurs as a contiguous subword (factor) an exact number of times and of the languages in which $w$…