Related papers: A Bibliography of Combinators
We discuss the role of combinators in the development of the modern conception of computation over the course of the past century. We describe how ideas about formalism and mathematical logic led to the introduction of combinators in 1920…
Combinators were a key idea in the development of mathematical logic and the emergence of the concept of universal computation. They were introduced on December 7, 1920, by Moses Sch\"onfinkel. This is an exploration of the personal story…
A partly autobiographical survey of the development of enumerative and algebraic combinatorics in the 1960's and 1970's.
We give a modern computational introduction to the S,K combinators invented by Moses Sch\"onfinkel in 1920, and present a variety of new results and ideas about combinators. We explore the spectrum of behavior obtained with small combinator…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
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…
To build a large library of mathematics, it seems more efficient to take advantage of the inherent structure of mathematical theories. Various theory presentation combinators have been proposed, and some have been implemented, in both…
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
We describe recent advances in the study of random analogues of combinatorial theorems.
We motivate and give semantics to theory presentation combinators as the foundational building blocks for a scalable library of theories. The key observation is that the category of contexts and fibered categories are the ideal theoretical…
This paper has been withdrawn.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…
This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…
This is an introduction to algebraic combinatorics, written for a quarter-long graduate course. It starts with a rigorous introduction to formal power series with some combinatorial applications, then discusses integer partitions (proving…
This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.
A survey written for the upcoming "Handbook of Enumerative Combinatorics".
The representations of the oscillator algebra introduced by Brzezinski et al. (Phys. Lett. B 311 (1993), 202) are classified.
The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory (through mid-2024) together with a summary of its results. We use a unified system of notation for the quantities being…
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable…
Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…