Related papers: Symmetric statistics on rational Dyck paths
A 3-dimensional Catalan word is a word on three letters so that the subword on any two letters is a Dyck path. For a given Dyck path $D$, a recently defined statistic counts the number of Catalan words with the property that any subword on…
The study of random walks has increasingly been popular across diverse disciplines such as statistics, mathematics, quantum physics, where they are used to model paths consisting of successive random steps in a mathematical space. A…
Motivated by problems arising in the relative trace formula and arithmetic invariant theory we prove the existence of rational points on orbits arising from certain infinitesimal symmetric spaces. As an application, we prove analogous…
We introduce square diagrams that represent numerical semigroups and we obtain an injection from the set of numerical semigroups into the set of Dyck paths.
The concepts of symmetric and asymmetric peaks in Dyck paths were introduced by Fl\'{o}rez and Ram\'{\i}rez, who counted the total number of such peaks over all Dyck paths of a given length. Elizalde generalized their results by giving…
A path integral representation is given for the solutions of the 3+1 dimensional Dirac equation. The regularity of the trajectories, the non-relativistic limit and the semiclassical approximation are briefly mentioned.
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
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 the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
In this paper we studied infinite weighted automata and a general methodology to solve a wide variety of classical lattice path counting problems in an uniform way. This counting problems are related to Dyck paths, Motzkin paths and some…
We introduce area, bounce and dinv statistics on decorated parallelogram polyominoes, and prove that some of their q,t-enumerators match $\langle \Delta_{h_m} e_{n+1},s_{k+1,1^{n-k}}\rangle$, extending in this way the work in (Aval et al.…
Given a Stirling permutation w, we introduce the mesa set of w as the natural generalization of the pinnacle set of a permutation. Our main results characterize admissible mesa sets and give closed enumerative formulas in terms of rational…
Regular Path Queries (RPQs) are a type of graph query where answers are pairs of nodes connected by a sequence of edges matching a regular expression. We study the techniques to process such queries on a distributed graph of data. While…
There is a natural bijection between Dyck paths and basis diagrams of the Temperley-Lieb algebra defined via tiling. Overhang paths are certain generalisations of Dyck paths allowing more general steps but restricted to a rectangle in the…
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…
We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a bijection proving this fact. Rushed paths turn out to be in…