Related papers: The combinatorics of Jeff Remmel
The concern of this paper is a famous combinatorial formula known under the name "exponential formula". It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential…
We provide a brief survey of a certain algebra of operators on symmetric polynomials, and collect a number of previously known results in the field.
We have compiled some sections of works by L. Zamick and collaborators which we hope will be of interest to the reader.
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
We present a proof of a combinatorial conjecture from the second author's Ph.D. thesis. The proof relies on binomial and multinomial sums identities. We also discuss the relevance of the conjecture in the context of PAC-Bayesian machine…
We prove several results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected…
The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
We discuss the significance of some interesting results by Barbara Rokowska about combinatorial constructions. Her interest in finite mathematics and number theory began with an embellishment and detailing of some work by Erdos. Rokowska…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
This paper constructs a combinatorial model for all postcritically finite rational maps arising as the Newton's method of a complex polynomial. This model is used in [LMS] to give a combinatorial classification of postcritically finite…
We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics and ideas particularly close to the interests of Jim Lambek.
Let A be a class of objects, equipped with an integer size such that for all n the number a(n) of objects of size n is finite. We are interested in the case where the generating fucntion sum_n a(n) t^n is rational, or more generally…
Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we…
Remarks on mathematical proof and the practice of mathematics.
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
Keller proposed a combinatorial conjecture on construction of an n-by-infinite matrix, which comes from showing the existence of many orbits of different sizes in certain linear group actions. He proved it for the case n=4, and we show that…
In this note we give some identities which involve the Mertens function M(n). Our proofs are combinatorial with relatively prime subsets as a main tool.
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some…