"It is shown that at least 50% of the probability mass of a sum of independent Rademacher random variables is within one standard deviation from its mean. This lower bound is sharp, it is much better than for instance the bound that can be obtained from application of the Chebishev inequality..."

"An alternate form for the binomial tail is presented, which leads to a variety of bounds for the central tail. A few can be weakened into the corresponding Chernoff and Slud bounds, which not only demonstrates the quality of the presented bounds, but also provides alternate proofs for the classical bounds."

"There are as many odd-sized as even-sized subsets sandwiched between two different sets."

Obsoletes Noga's recent result.

"The usual Azuma's inequality assumes absolute bounds on the Martingale differences. This is often too pessimistic, but seems inherently required in the usual moment-generating function method. We prove a new general inequality based on bounds on moments of Martingale differences rather than absolute bounds; while the method used is elementary, it is quite different from the m-g f method."

"We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\'an's theorem, Szemer\'edi's theorem and Ramsey's theorem, hold almost surely inside sparse random sets."

The techniques taught early on in "Probability Theory and Combinatorial Optimization" apparently go quite far.

"Most of the works mentioned below focus on combinatorial properties, and specifically on graph properties. The two standard representations of graphs - by adjacency matrix and by incidence lists - yield two different models for testing graph properties. In the first model graphs, most appropriate for dense graphs, distance between N-vertex graphs is measured as the fraction of edges on which the graphs disagree over N^2. In the second model graphs, most appropriate for bounded-degree graphs, distance between N-vertex d-degree graphs is measured as the fraction of edges on which the graphs disagree over dN."

Free online book by an upcoming seminar speaker. "We develop in about 800 pages the basics of asymptotic enumeration and the analysis of random combinatorial structures through an approach that revolves around generating functions and complex analysis."

The coefficient extraction method and its predecessor the constant term method.

Workshop at Texas A&M.

Ordinary and exponential generating functions are useful for determining the properties of random permutations.