We construct 2Ω(n 5/4) combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2O(n log n) combinatorial types of simplicial 4-polytopes, this proves that asymptotically, there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988...

Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. “Singularity analysis” reviewed here provides constructive estimates that are applicable in several areas...

1 Flajolet, P. and M. Soria, General combinatorial schemas: Gaussian limit distributions and exponential tails, Discrete Mathematics 114 (1993) 159-180. Under general conditions, the number of components in combinatorial structures defined as sequences, cycles or sets of components admits a Gaussian limit distribution together with an exponential tail. The results are valid, assuming simple ana...

human snake bitten poisoning is a serious threat in many tropical and subtropical countries such as iran. the best acceptable treatment of envenomated humans is antivenoms; however they have a series of economic and medical problems and need more improvements. in this study a combinatorial human immunoglobulin gene library against some of iranian snakes venoms was constructed. total rna prepare...

We consider the class of L-convex polyominoes, i.e. convex polyominoes where any two chosen cells can be connected simply using an internal path having at most one change of direction. The main result of the paper is the definition of an object grammar decomposition of this class, which gives combinatorial evidence of the rationality of the generating function, and suggests some new combinatori...

In combinatorial number theory, there are many topics related to group structure. Even for abelian or cyclic groups, there are some very challenging unsolved conjectures. In this talk we give a survey of problems, results and methods in several fields of combinatorial number theory. The topics include sumsets in additive combinatorics, Snevily’s conjecture and Latin transversals, covers of the ...

" Mathematicians care no more for logic than logicians for mathematics. " Augustus de Morgan, 1868 Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition ...

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind. 2010 Mathematics Subject Classification: Primary 34A05; Secondary 11B37, 34A34.

We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a definable set. We prove that some consequences of Ramsey’s Theorem for colorings of pairs could help in simplifying the definitions of some Δ2 sets, while some oth...

My research is situated at the interface of algebraic combinatorics, representation theory, algebraic geometry, and algebraic topology. It focuses on developing new combinatorial structures and methods for computation, particularly related to the representation theory of Lie algebras and modern Schubert calculus on flag manifolds. Thus, my work is part of the current trend in mathematics which ...