Related papers: The B. B. Newman Spelling Theorem
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem rely on labelled trees, whereas recent developments in…
B-terms are built from the B combinator alone defined by B f g x = f (g x), which is well-known as a function composition operator. This paper investigates an interesting property of B-terms, that is, whether repetitive right applications…
In this paper, we study a combinatorial problem originating in the following conjecture of Erdos and Lemke: given any sequence of n divisors of n, repetitions being allowed, there exists a subsequence the elements of which are summing to n.…
The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, such as…
The topic of this treatise is a combinatorial technique called Graph Pebbling. We investigate pebbling numbers, weight functions, flow networks, hypercubes, and the zero-sum conjecture of Erd\H{o}s and Lemke. This investigation is a…
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties…
A unified theory of language combines a Bayesian cognitive linguistic model of language processing, with the proposal that language evolved by sexual selection for the display of intelligence. The theory accounts for the major facts of…
The material of the article is devoted to the most complicated and interesting problem -- a problem of P = NP?. This research was presented to mathematical community in Hyderabad during International Congress of Mathematicians. But there it…
The Bateman-Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green-Tao theorem, along with many famous conjectures, such the…
In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…
The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with…
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph…
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…
This survey is intended to provide an overview of one of the oldest and most celebrated open problems in combinatorial algebra: the word problem for one-relation monoids. We provide a history of the problem starting in 1914, and give a…
A theory of language learning is described, which uses Bayesian induction of feature structures (scripts) and script functions. Each word sense in a language is mentally represented by an m-script, a script function which embodies all the…
We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the…
$B$-terms are built from the $B$ combinator alone defined by $B\equiv\lambda fgx. f(g~x)$, which is well known as a function composition operator. This paper investigates an interesting property of $B$-terms, that is, whether repetitive…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…