Related papers: Generating trees growing on the left for pattern-a…
We use combinatorial and generating function techniques to enumerate various sets of involutions which avoid 231 or contain 231 exactly once. Interestingly, many of these enumerations can be given in terms of $k$-generalized Fibonacci…
We consider simply generated trees and study multiplicative functions on rooted plane trees. We show that the associated generating functions satisfy differential equations or difference equations. Our approach considers B-series from…
Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional…
In this work a method is presented to derive the generating functional in path integral form for a system with an arbitrary number of degrees of freedom and constrained by general conditions. The method is applied to the case of the…
Most existing text generation models follow the sequence-to-sequence paradigm. Generative Grammar suggests that humans generate natural language texts by learning language grammar. We propose a syntax-guided generation schema, which…
A syntax tree is a planar rooted tree where internal nodes are labeled on a graded set of generators. There is a natural notion of occurrence of contiguous pattern in such trees. We describe a way, given a set of generators $\mathfrak{G}$…
We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the…
A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special…
The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous…
Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a…
Despite the fact that the field of pattern avoiding permutations has been skyrocketing over the last two decades, there are very few exhaustive generating algorithms for such classes of permutations. In this paper we introduce the notions…
In this paper we find the generating function for the number of vertices that have k elements in their subtree and use this generating function to calculate the probability that a vertex has a size k subtree. We also show how this same…
We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples…
Neural sequence generation is typically performed token-by-token and left-to-right. Whenever a token is generated only previously produced tokens are taken into consideration. In contrast, for problems such as sequence classification,…
In this paper, we introduce a new method for computing generating functions with respect to the number of descents and left-to-right minima over the set of permutations which have no consecutive occurrences of a pattern that starts with 1.
In this paper we study substitutions and some of their associated generating functions. This association takes aperiodicity to transcendence, and vice-versa. These generating functions have a recursive structure arising from the…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
Analysis of probability distributions conditional on species trees has demonstrated the existence of anomalous ranked gene trees (ARGTs), ranked gene trees that are more probable than the ranked gene tree that accords with the ranked…