Related papers: Complexity problems in enumerative combinatorics

We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.

We discuss some of the problems that may occur in the calculation of complicated Feynman diagrams. These include the group independent evaluation of color factors, and the summation techniques that are needed for the expansion of diagrams…

We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is…

This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…

We find an abundance of Cremer Julia sets of an arbitrarily high computational complexity.

Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…

We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…

We survey recent results on combinatorial optimization problems in which the objective function is the entropy of a discrete distribution. These include the minimum entropy set cover, minimum entropy orientation, and minimum entropy…

We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and…

This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

We introduce and investigate a series of matching problems for patterns with variables under Simon's congruence. Our results provide a thorough picture of these problems' computational complexity.

We describe some combinatorial problems in finite projective planes and indicate how R\'edei's theory of lacunary polynomials can be applied to them.

This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…

The paper proposes open problems in classical Kolmogorov complexity. Each problem is presented with background information and thus the article also surveys some recent studies in the area.

Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is very fast developing, and in this long but relatively short survey we select some of those results which either we feel very important in this field or which…

Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…

We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for…

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…