Related papers: Pure O-sequences: known results, applications, and…
In this paper, we study sequences of positive numbers preserving summability. In particular, the open set property for such a family of sequences is shown. Several classes of sequences preserving summability, including polynomials, sums of…
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…
This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence…
We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of $n\times n$ matrices with entries that are polynomials or more…
We present and discuss seven different open problems in applied combinatorics. The application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods,…
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
Some Open Problems Concerning Orthogonal Polynomials.
Investigation on open questions about perturbation of Hermitian sequences and their spectral symbols. Results on normal sequences are also furnished.
These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…
This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.