Related papers: Pattern avoidance in labelled trees

This article introduces an analogue of permutation classes in the context of polyominoes. For both permutation classes and polyomino classes, we present an original way of characterizing them by avoidance constraints (namely, with excluded…

Partially ordered patterns (POPs) generalize the classical notion of permutation patterns within the framework of pattern avoidance. Building on recent work by Burstein, Han, Kitaev, and Zhang, which introduced the concept of…

We study the distribution and the popularity of left children on sets of treeshelves avoiding a pattern of size three. (Treeshelves are ordered binary increasing trees where every child is connected to its parent by a left or a right link.)…

In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…

The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…

Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…

We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational…

The purpose of this paper is twofold. First we answer to a question asked by Steingrimsson and Williams about certain permutation tableaux: we construct a bijection between binary trees and the so-called Catalan tableaux. These tableaux are…

We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…

In 2012, Sagan and Savage introduced the notion of $st$-Wilf equivalence for a statistic $st$ and for sets of permutations that avoid particular permutation patterns which can be extended to generalized permutation patterns. In this paper…

We enumerate and characterize some classes of alternating and reverse alternating involutions avoiding a single pattern of length three or four. If on one hand the case of patterns of length three is trivial, on the other hand, the length…

Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…

For permutations avoiding consecutive patterns from a given set, we present a combinatorial formula for the multiplicative inverse of the corresponding exponential generating function. The formula comes from homological algebra…

We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli…

Patterns describe proven solutions for recurring problems. Typically, patterns in a particular domain are interrelated and organized in pattern languages. As real-world problems often require patterns of multiple domains, different pattern…

We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices…

A set partition avoids a pattern if no subdivision of that partition standardizes to the pattern. There exists a bijection between set partitions and restricted growth functions (RGFs) on which Wachs and White defined four statistics of…

Tabular foundation models with different architectures converge in accuracy across a range of classification and regression tasks. This raises questions a leaderboard cannot answer: (i) whether the models execute the same in-context…

Dependency trees have proven to be a very successful model to represent the syntactic structure of sentences of human languages. In these structures, vertices are words and edges connect syntactically-dependent words. The tendency of these…

Recent work on the problem of latent tree learning has made it possible to train neural networks that learn to both parse a sentence and use the resulting parse to interpret the sentence, all without exposure to ground-truth parse trees at…