Related papers: Dispersed Dyck paths revisited
A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
Molecular spiders are synthetic bio-molecular systems which have "legs" made of short single-stranded segments of DNA. Spiders move on a surface covered with single-stranded DNA segments complementary to legs. Different mappings are…
Paths in a given network are a generalised form of time-serial chains in many real-world applications, such as trajectories and Internet flows. Differentially private trajectory publishing concerns publishing path information that is usable…
A crinkled subordinator is an $\ell^2$-valued random process which can be thought of as a version of the usual one-dimensional subordinator with each out of countably many jumps being in a direction orthogonal to the directions of all other…
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…
We present a family of distributed forward-backward methods with variable stepsizes to find a solution of structured monotone inclusion problems. The framework is constructed by means of relocated fixed-point iterations, extending the…
In this paper, we introduce directed networks called `divergence network' in order to perform graphical calculation of divergence functions. By using the divergence networks, we can easily understand the geometric meaning of calculation…
We define and study dispersionless coupled modified KP hierarchy, which incorporates two different versions of dispersionless modified KP hierarchies.
We determine some of the derived equivalences of a class of gentle algebras called surface algebras. These algebras are constructed from an unpunctured Riemann surface of genus 0 with boundary and marked points by introducing cuts in…
The theme of this article is a "reciprocity" between bounded up-down paths and bounded alternating sequences. Roughly speaking, this ``reciprocity" manifests itself by the fact that the extension of the sequence of numbers of paths of…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…
Divisible design digraphs which can be obtained as Cayley digraphs are studied. A characterization of divisible design Cayley digraphs in terms of the generating sets is given. Further, we give several constructions of divisible design…
Flip graphs of non-crossing configurations in the plane are widely studied objects, e.g., flip graph of triangulations, spanning trees, Hamiltonian cycles, and perfect matchings. Typically, it is an easy exercise to prove connectivity of a…
Garsia and Xin gave a linear algorithm for inverting the sweep map for Fuss rational Dyck paths in $D_{m,n}$ where $m=kn\pm 1$. They introduced an intermediate family $\mathcal{T}_n^k$ of certain standard Young tableau. Then inverting the…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
The classical Chung-Feller theorem [2] tells us that the number of Dyck paths of length $n$ with $m$ flaws is the $n$-th Catalan number and independent on $m$. In this paper, we consider the refinements of Dyck paths with flaws by four…
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve,…
The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two…
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…