Related papers: Normal ordering problem and the extensions of the …
Recently, Haglund and Visontai established the stability of the multivariate Eulerian polynomials as the generating polynomials of the Stirling permutations, which serves as a unification of some results of B\'{o}na, Brenti, Janson, Kuba,…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
In this paper, we consider a generalization of the Stirling number sequence of both kinds by using a specialization of a new family of symmetric functions. We give combinatorial interpretations for this symmetric functions by means of…
In this paper we provide a unified combinatorial approach to establish a connection between Stirling permutations, cycle structures of permutations and perfect matchings. The main tool of our investigations is MY-sequences. In particular,…
We present a new class of binary words: the prefix normal words. They are defined by the property that for any given length $k$, no factor of length $k$ has more $a$'s than the prefix of the same length. These words arise in the context of…
We introduce a normal form for context-free grammars, called Dyck normal form. This is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired nonterminals.…
We address a systematic combinatorial approach to the anti-normal ordering problem. In this way, we use the Stirling numbers and their generating function, the so-called Bell polynomials, together with the operational methods to anti-normal…
We define a new family of generalized Stirling permutations that can be interpreted in terms of ordered trees and forests. We prove that the number of generalized Stirling permutations with a fixed number of ascents is given by a natural…
Many natural counting problems arise in connection with the normal form of braids--and seem to have never been considered so far. Here we solve some of them by analysing the normality condition in terms of the associated permutations, their…
Regular word grammars are restricted context-free grammars that define all the recognizable languages of words. This paper generalizes regular grammars from words to certain classes of graphs, by defining regular grammars for unordered…
We show that it is decidable in exponential time whether the lexicographic ordering of a context-free language is scattered, or a well-ordering.
We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
The aim of this paper is to study the $\lambda$-Stirling numbers of both kinds which are $\lambda$-analogues of Stirling numbers of both kinds. Those numbers have nice combinatorial interpretations when $\lambda$ are positive integers. If…
The normal ordering coefficients of strings consisting of $V,U$ which satisfy $UV=qVU+hV^s$ ($s\in\mathbb N$) are considered. These coefficients are studied in two contexts: first, as a multiple of a sequence satisfying a generalized…
This paper describes a pattern to formalise context-free grammars in OWL and its use for sequence classification. The proposed approach is compared to existing methods in terms of computational complexity as well as pragmatic applicability,…
We introduce new refinements of the Bell, factorial, and unsigned Stirling numbers of the first and second kind that unite the derangement, involution, associated factorial, associated Bell, incomplete Stirling, restricted factorial,…
In this article combinatorial aspects of normal ordering annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled since otherwise the problem of normal ordering is reduced to the…
Given an ordered set partition, when one insert a number of bars in-between the blocks of the ordered set partition the result is a barred preferential arrangement. In this study, using the notion of barred preferential arrangements we…
Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…