Related papers: An Introduction to Combinatorics of Determinacy
A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n + 1 into parts greater than one. Some commentary about the history of partitions and compositions is…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
The following thesis contains results on the combinatorial representation theory of the finite Hecke algebra $H_n(q)$. In Chapter 2 simple combinatorial descriptions are given which determine when a Specht module corresponding to a…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…
We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
We define and study expansion problems on countable structures in the setting of descriptive combinatorics. We consider both expansions on countable Borel equivalence relations and on countable groups, in the Borel, measure and category…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics. Background details, definitions and motivations are also provided.
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Extensions of a set partition obtained by imposing bounds on the size of the parts and the coloring of some of the elements are examined. Combinatorial properties and the generating functions of some counting sequences associated with these…
It has become obvious in the recent development that the structural Ramsey property is a categorical property: it depends not only on the choice of objects, but also on the choice of morphisms involved. In this paper we explicitely put the…
Bar Codes are combinatorial objects encoding many properties of monomial ideals. In this paper we employ these objects to study Janet-like divisions. Given a finite set of terms U, from its Bar Code we can compute the Janet-like…
We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness.…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…