My expertise falls primarily into the categories of enumerative, probabilistic, and graph
theoretic combinatorics. My undergraduate and master's level study under Dr. Thomas …

The converse of the Borel–Cantelli Lemma states that if {A i} i= 1∞ is a sequence of
independent events such that∑ P (A i)=∞, then almost surely infinitely many of these events …

A classic and fundamental result, known as the Lovász Local Lemma, is a gem in the
probabilistic method of combinatorics. At a high level, its core message can be described by …

The Lovász local lemma is a powerful and well-studied probabilistic technique useful in
establishing the possibility of simultaneously avoiding every event in some collection. A …

The Lovász local lemma is a well-known probabilistic technique commonly used to prove
the existence of rare combinatorial objects. We explore the lopsided (or negative …

This paper presents an offering of some of the myriad connections between Combinatorics
and Probability, directed in particular toward combinatorialists. The choice of material was …

In the first two editions of the book “Probability,” which appeared in 1980 and 1989 (see
[118]), and were translated into English in 1984 and 1990 (see [119]), all chapters were …

The Lov\'asz Local Lemma is a seminal result in probabilistic combinatorics. It gives a
sufficient condition on a probability space and a collection of events for the existence of an …

The concept of independence in probability, called stochastic independence, was
introduced early in the history of the topic. If events form an independent class, then the …

Perhaps combinatorics is no longer deemed to be the slum of topology but it still has a
remarkable polarising effect on mathematicians. The practitioners of combinatorics tend to …