In this paper, uniform designs are constructed based on nearly U-type designs and the discrete discrepancy. The link between such uniform designs and resolvable packings and coverings in combinatorial design theory is developed. Through resolvable packings and coverings without identical parallel classes, many infinite classes of new uniform designs are then produced.

The class will focus on two themes: linear algebra and probability, and their many applications in algorithm design. We will cover a number of classical examples, including: fast matrix multiplication, FFT, error correcting codes, cryptography, efficient data structures, combinatorial optimization, routing, and more. We assume basic familiarity (undergraduate level) with linear algebra, probabi...

We present empirical results on computing optimal dominating sets in networks by means of data reduction through preprocessing rules. Thus, we demonstrate the usefulness of so far only theoretically considered reduction techniques for practically solving one of the most important network problems in combinatorial optimization. keywords Graph Theory, Location, Topological Design, Network Models,...

the multivariate exponentially weighted moving average (mewma) control chart is one of the best statistical control chart that are usually used to detect simultaneous small deviations on the mean of more than one cross-correlated quality characteristics. the economic design of mewma control charts involves solving a combinatorial optimization model that is composed of a nonlinear cost function ...

In this article we give an overview of a line of research in set theory that has reached a level of maturity and which, in our opinion, merits its being exposed to a more general audience. This line of research is concentrated on finding to which extent compactness fails at the level of first uncountable cardinal and to which extent it could be recovered at the level of some other not so large ...

“Combinatorial number theory”, in very loose terms, can be described as an area of mathematics which is a cross between combinatorics and number theory. More precisely, the area concerns structures of integers (or similar sets), with some number theoretic properties, which can be studied mainly by combinatorial means, rather than, for example, by algebraic methods. This area really only truly e...

My primary research interest is in the interplay between combinatorics and algebraic structures. By employing combinatorial tools such as symmetric functions, partitions, tableaux, graphs, posets, and crystal bases, one can gain significant insight on algebraic and geometric structures such as groups, algebras and rings; and, conversely, the corresponding structure theory can often lead to surp...

The matroid is called loopless if the empty subset of E is closed, and is called a combinatorial geometry if in addition all single element subsets of E are closed. A closed subset of E is called a flat of M, and every subset of E has a well-defined rank and corank in the poset of all flats of M. The notion of matroid played a fundamental role in graph theory, coding theory, combinatorial optim...

1 Introduction. Homotopy theory is a subdomain of topology where, instead of considering the category of topological spaces and continuous maps, you prefer to consider as morphisms only the continuous maps up to homotopy, a notion precisely defined in these notes in Section 4. Roughly speaking, you decide not to distinguish two maps which can be continuously deformed into each other; such a wea...

The Combinatorial Nullstellensatz is a theorem about the roots of a polynomial. It is related to Hilbert’s Nullstellensatz. Established in 1996 by Alon et al. [4] and generalized in 1999 by Alon [2], the Combinatorial Nullstellensatz is a powerful tool that allows the use of polynomials to solve problems in number theory and graph theory. This article introduces the Combinatorial Nullstellensat...