Recent Results on Difference Sets with Classical Parameters

TL;DR: A well-rounded treatment of non-Boolean functions with optimal nonlinearity is given, which summarizes and generalizes known results, and proves a number of new results.

TL;DR: The best known value for the asymptotic merit factor has remained unchanged since 1988 as discussed by the authors, but recent experimental and theoretical results strongly suggest a possible improvement, and a survey describes the development of the merit factor problem by bringing together results from several disciplines, and places the recent results within their historical and scientific framework.

TL;DR: This survey describes the development of the understanding of the merit factor problem by bringing together results from several disciplines, and places the recent results within their historical and scientific framework.

TL;DR: A well rounded treatment of binary sequences with optimal autocorrelation is given.

Abstract: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.

TL;DR: The first properties of the plane can be found in this article, where the authors define the following properties: 1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. Ovals 9. Arithmetic of arcs of degree two 10. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes 15.

TL;DR: In this article, it was shown that there is always at least one collineation of period q with respect to any point in the projective plane PG(2, pn) for every prime p and positive integer n.