相关论文: A Grammatical Calculus for Peaks and Runs of Permu…

We generalize the concept of ascending and descending runs from permutations to rooted labelled trees and mappings, i.e., functions from the set $\{1, \dots, n\}$ into itself. A combinatorial decomposition of the corresponding functional…

In this paper, we introduce the notion of a grammatical labeling to describe a recursive process of generating combinatorial objects based on a context-free grammar. For example, by labeling the ascents and descents of a Stirling…

Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…

This paper is concerned with the joint distribution of the number of exterior peaks and the number of proper double descents over permutations on $[n] =\{1,2,\ldots,n\}$. The notion of exterior peaks of a permutation was introduced by…

Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.

In this work we obtain recurrent formulae for the number of permutations with either increasing or monotonic (i.e., both increasing and decreasing) runs of bounded length. Our formulae allow one to efficiently compute the number of such…

Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence…

This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…

Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture…

Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…

In his Ph.D. thesis, Ira Gessel proved a reciprocity formula for noncommutative symmetric functions which enables one to count words and permutations with restrictions on the lengths of their increasing runs. We generalize Gessel's theorem…

In this paper, we focus on the enumeration of permutations by number of cyclic occurrence of peaks and valleys. We find several recurrence relations involving the number of permutations with a prescribed number of cyclic peaks, cyclic…

The Ramanujan polynomials arise in three intertwined contexts. As remarked by BerndtEvans-Wilson, no combinatorial perspective seems to be alluded to in the original definition of Ramanujan. On a different stage, Dumont-Ramamonjisoa…

Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…

Derivative polynomials in two variables are defined by repeated differentiation of the tangent and secant functions. We establish the connections between the coefficients of these derivative polynomials and the numbers of interior and left…

Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…

Grammatic is a tool for grammar definition and manipulation aimed to improve modularity and reuse of grammars and related development artifacts. It is independent from parsing technology and any other details of target system…

We implement a divide-and-concur iterative projection approach to context-free grammar inference. Unlike most state-of-the-art models of natural language processing, our method requires a relatively small number of discrete parameters,…

The mechanisms of comprehension during language processing remains an open question. Classically, building the meaning of a linguistic utterance is said to be incremental, step-by-step, based on a compositional process. However, many…

The grammar representation of a narrowing tree for a syntactically deterministic conditional term rewriting system and a pair of terms is a regular tree grammar that generates expressions for substitutions obtained by all possible…