Tree theory, partitions of integer numbers, combinatorial mathematics and computer algebra are the basis for the construction of a powerful and efficient symbolic package for the derivation of Runge Kutta order conditions and principal truncation error terms.

This is a short survey of algebro-combinatorial link homology theories which have the Jones polynomial and other link polynomials as their Euler characteristics. 2000 Mathematics Subject Classification: 57M25, 57Q45.

We argue that combinatorial maps theory is mathematical challenge that is not sufficiently developed but rather is some unreasonably unattended or weakly supported by interest of researchers area of mathematics.

s of invited talks Metamorphoses of graph designs Elizabeth J. Billington University of Queensland A lambda-fold graph design, or G-design of order n, is an edge-disjoint decomposition of a λ-fold complete graph, λKn, into isomorphic copies of some graph G. (Here λKn denotes the graph on n vertices with precisely λ edges between every pair of vertices.) Let H be a subgraph of G. A metamorphosis...

We give a combinatorial proof of the inequality in the title in terms of Fibonacci numbers and Euler numbers. The result is motivated by Sidorenko’s theorem on the number of linear extensions of the poset and its complement. We conclude with some open problems. November 5, 2016. ⋆Department of Mathematics, UCLA, LA, CA 90095. Email: {ahmorales,pak}@math.ucla.edu. Department of Mathematics, UPen...

In this paper we show how certain notions of modern cryptogra phy can be presented to youngsters using combinatorial constructions Among the topics discussed are the use of Boolean circuits for bit com mitment protocols and hash functions and the construction of a public key message transmission system using perfect codes in a graph We also discuss how e orts such as this in popularizing mathem...

Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familiar examples of regular maps. The great dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps ...

It is very fortunate that two, and sometimes three, sessions of the Séminaire Lotharingien have been held every year since its beginning in 1980. Otherwise, several of us, at least the confirmed optimists, would have witnessed the jubilee in Paradise! Anyway, this is a great privilege to have all of you here, at the Domaine Saint-Jacques, a place regarded as a valeur sûre by the younger generat...

ESSENCE is a new formal language for specifying combinatorial problems in a manner similar to natural rigorous specifications that use a mixture of natural language and discrete mathematics. ESSENCE provides a high level of abstraction, much of which is the consequence of the provision of decision variables whose values can be combinatorial objects, such as tuples, sets, multisets, relations, p...

My research uses algebraic and geometric methods to prove theorems in extremal combinatorics. Going the other way, I also use combinatorial methods to prove algebraic results. Algebraic methods are deeply embedded in my work and nearly all of my success in graph theoretic research has come from attacking purely combinatorial problems through the lens of algebra, combinatorial number theory, or ...