Related papers: Rectangular Young tableaux with local decreases an…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
We introduce an object called a decorated Young tableau which can equivalently be viewed as a continuous time trajectory of Young diagrams or as a non-intersecting line ensemble. By a natural extension of the Robinson-Schensted…
In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
In this paper, we propose generative probabilistic models for label aggregation. We use Gibbs sampling and a novel variational inference algorithm to perform the posterior inference. Empirical results show that our methods consistently…
We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…
A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…
Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy…
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms…
In materials science, the challenge of rapid prototyping materials with desired properties often involves extensive experimentation to find suitable microstructures. Additionally, finding microstructures for given properties is typically an…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework…
We present a generating function and a closed counting formula in two variables that enumerate a family of classes of permutations that avoid or contain an increasing pattern of length three and have a prescribed number of occurrences of…
A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For…
In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
Young tableaux are combinatorial objects whose construction can be achieved from words over a finite alphabet by row or column insertion as shown by Schensted sixty years ago. Recently Abram and Reutenauer studied the action the free monoid…