Related papers: Random 3-noncrossing partitions
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here, we derive the first-crossing distribution of random walks with a…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm which we used to obtain first examples of so-called non-easy linear categories of…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
A triangular partition is a partition whose Ferrers diagram can be separated from its complement (as a subset of $\mathbb{N}^2$) by a straight line. Having their origins in combinatorial number theory and computer vision, triangular…
In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints (also called constrained non-crossing Laman frameworks) on a given…
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population…
This paper gives a new algorithm for sampling tree-weighted partitions of a large class of planar graphs. Formally, the tree-weighted distribution on $k$-partitions of a graph weights $k$-partitions proportional to the product of the number…
We compute the representation theory of two families of noncrossing partition quantum groups connected to amalgamated free products and free wreath products. This illustrates the efficiency of the methods developed in our previous joint…
A trigraph is a graph where each pair of vertices is labelled either 0 (a non-arc), 1 (an arc) or $\star$ (both an arc and a non-arc). In a series of papers, Hell and co-authors proposed to study the complexity of homomorphisms from graphs…
In a geometric inhomogeneous random graph vertices are given by the points of a Poisson process and are equipped with independent weights following a heavy tailed distribution. Any pair of distinct vertices is independently forming an edge…
Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…
Higher-order notions of Kreweras complementation have appeared in the literature in the works of Krawczyk, Speicher, Mastnak, Nica, Arizmendi, Vargas, and others. While the theory has been developed primarily for specific applications in…
For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…
The notion of containment and avoidance provides a natural partial ordering on set partitions. Work of Sagan and of Goyt has led to enumerative results in avoidance classes of set partitions, which were refined by Dahlberg et al. through…
Although exchangeable processes from Bayesian nonparametrics have been used as a generating mechanism for random partition models, we deviate from this paradigm to explicitly incorporate clustering information in the formulation of our…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…