Submodular functions are discrete analogue of convex functions, arising in various fields of applied mathematics including game theory, information theory, and queueing theory. This survey aims at providing an overview on fundamental properties of submodular functions and recent algorithmic developments of their optimization and approximation. For submodular function minimization, the ellipsoid...

These Smarandache spaces are right theories for objectives by logic. However, the mathematical combinatorics is a combinatorial theory for branches in classical mathematics motivated by a combinatorial speculation. Both of them are unifying theories for sciences and contribute more and more to mathematics in the 21st century. In this paper, I introduce these two subjects and mainly concentrate ...

Wachs, M.L. The major index polynomial for conjugacy classes of permutations, Discrete Mathematics 91 (1991) 283-293. Garsia (1988) gives a remarkably simple expression for the major index enumerator for permutations of a fixed cycle type evaluated at a primitive root of unity. He asks for a direct combinatorial proof of this identity. Here we give such a combinatorial derivation.

With this article I want to take the opportunity to sketch the development of topological proofs in discrete mathematics beginning with the proof of the Kneser conjecture about 25 years ago, which eventually led to a new discipline: topological combinatorics. In the beginning of the twentieth century the discipline of combinatorial topology already made use of combinatorial concepts in topology...

Chung, F., P. Diaconis and R. Graham, Universal cycles for combinatorial structures, Discrete Mathematics 110 (1992) 43-59 In this paper, we explore generalizations of de Bruijn cycles for a variety of families of combinatorial structures, including permutations, partitions and subsets of a finite set.

In general, in the midst of History Mathematics textbooks, we are faced with a discussion due to curiosity about emblematic Fibonacci Sequence, whose popularization occurred proposition reproduction model immortal rabbits. On other hand, comparison multiple approaches and discussions certain subjects Elementary Mathematics, present work, highlight combinatorial interpretations that, support cha...

The time is ripe to start a science of identities for their own sake, without paying lip-service to high-brow mathematics. Although putting combinatorial, (abstract-) algebraic or analytic flesh and blood on identities did lead and will lead to considerable insight as well as new identities, there is also much to be gained in forgetting advanced mathematics, and starting a new sub-discipline of...

Anne Pieper currently teaches high school geometry at The Westminster Schools in Atlanta, Georgia. She recently graduated fromThe University of Georgia with an M.A. in Mathematics Education. Current trends in the revision of both mathematics curricula and traditional teaching strategies include the incorporation of discrete mathematics into the secondary school curriculum (Dossey, 1990). Seriou...

His talent for mathematics was evident from his high-school years when he won the second and first prize of the Romanian Mathematics Olympiads in 1959 and 1960. Later on, he was awarded the " Applied Mathematics Prize " at the First Balkan Mathematics Competition for Students and Young Researchers (1971) and the " Gheorghe T ¸ it¸eica Prize " of the Romanian Academy (1975). Professor Tomescu's ...