The Probabilistic Method in Combinatorics
نویسنده
چکیده
2 The Linearity of Expectation and small tweakings 11 2.1 Revisiting the Ramsey Number R(n, n) . . . . . . . . . . . . . . . . . . . 11 2.2 List Chromatic Number and minimum degree . . . . . . . . . . . . . . . 11 2.3 The Daykin-Erdős conjecture . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 An Example from Combinatorial Geometry . . . . . . . . . . . . . . . . . 14 2.5 Graphs with High Girth and High Chromatic Number . . . . . . . . . . . 14
منابع مشابه
A Probabilistic Technique for Finding Almost-periods in Additive Combinatorics
We introduce a new probabilistic technique for finding ‘almost-periods’ of convolutions of subsets of finite groups. This allows us to give probabilistic proofs of two classical results in additive combinatorics: Roth’s theorem on three-term arithmetic progressions and the existence of long arithmetic progressions in sumsets A+B in Zp. The bounds we obtain for these results are not the best one...
متن کاملPaul Erdős and Probabilistic Reasoning
One of the major contributions of Paul Erdős is the development of the Probabilistic Method and its applications in Combinatorics, Graph Theory, Additive Number Theory and Combinatorial Geometry. This short paper describes some of the beautiful applications of the method, focusing on the long-term impact of the work, questions and results of Erdős. This is mostly a survey, but it contains a few...
متن کاملProbabilistic and Extremal Combinatorics∗ Organizers
Combinatorics, sometimes also called Discrete Mathematics, is a branch of mathematics focusing on the study of discrete objects and their properties. Although Combinatorics is probably as old as the human ability to count, the field experienced tremendous growth during the last fifty years and has matured into a thriving area with its own set of problems, approaches and methodology. Extremal an...
متن کاملWorkshop: Combinatorics, Probability and Computing Table of Contents
One of the exciting phenomena in mathematics in recent years has been the widespread and surprisingly effective use of probabilistic methods in diverse areas. The probabilistic point of view has turned out to be very profitable in Discrete Mathematics, Analysis and Theoretical Computer Science. The meeting was dedicated to recent developments in these areas, focusing on the investigation of ran...
متن کاملOrthogonal Latin Rectangles
We use a greedy probabilistic method to prove that for every > 0, every m × n Latin rectangle on n symbols has an orthogonal mate, where m = (1− )n. That is, we show the existence of a second latin rectangle such that no pair of the mn cells receives the same pair of symbols in the two rectangles.
متن کاملProbabilistic analysis of stability of chain pillars in Tabas coal mine in Iran using Monte Carlo simulation
Performing a probabilistic study rather than a determinist one is a relatively easy way to quantify the uncertainty in an engineering design. Due to the complexity and poor accuracy of the statistical moment methods, the Monte Carlo simulation (MCS) method is wildly used in an engineering design. In this work, an MCS-based reliability analysis was carried out for the stability of the chain pill...
متن کامل