Related papers: Generating sequences and key polynomials
Descriptive titles provide crucial context for interpreting tables that are extracted from web pages and are a key component of table-based web applications. Prior approaches have attempted to produce titles by selecting existing text…
We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
Keyphrases are a very short summary of an input text and provide the main subjects discussed in the text. Keyphrase extraction is a useful upstream task and can be used in various natural language processing problems, for example, text…
The aim of this paper is to construct general forms of ordinary generating functions for special numbers and polynomials involving Fibonacci type numbers and polynomials, Lucas numbers and polynomials, Chebyshev polynomials, Sextet…
In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…
Divide-and-conquer functions satisfy equations in F(z),F(z^2),F(z^4)... Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By…
Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…
Definition Modeling, the task of generating definitions, was first proposed as a means to evaluate the semantic quality of word embeddings-a coherent lexical semantic representations of a word in context should contain all the information…
We construct generating trees with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation,…
Assessing generative models is not an easy task. Generative models should synthesize graphs which are not replicates of real networks but show topological features similar to real graphs. We introduce an approach for assessing graph…
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
The article is an attempt to contribute to explorations of a common origin for language and planned-collaborative action. It gives `semantics of change' the central stage in the synthesis, from its history and recordkeeping to its…
We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…
This thesis investigates the generation of new concepts from combinations of existing concepts as a language evolves. We give a method for combining concepts, and will be investigating the utility of composite concepts in language evolution…
In this work we define a unified generating functions for 9 different kinds of set partitions including cyclically ordered set partitions. Such generating function depends on 4 parameters. We consider property of this function and provide…
An important component of achieving language understanding is mastering the composition of sentence meaning, but an immediate challenge to solving this problem is the opacity of sentence vector representations produced by current neural…
The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree…