Computing and Combinatorics

The Subset Partial Order: Computing and Combinatorics

Given a family F of k sets with cardinalities s1, s2, . . . , sk and N = ∑ k i=1 si, we show that the size of the partial order graph induced by the subset relation (called the subset graph) is O( ∑ si≤B 2i + N/ logN · ∑ si>B log (2si/B)), where B = log (N/ log N). This implies a simpler proof to the O(N/ log N) bound concluded in [2]. We also give an algorithm that computes the subset graph fo...

Workshop: 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...

Combinatorics Enumerative Combinatorics 05

Analytic Combinatorics — Symbolic Combinatorics

This booklet develops in nearly 200 pages the basics of combinatorial enumeration through an approach that revolves around generating functions. The major objects of interest here are words, trees, graphs, and permutations, which surface recurrently in all areas of discrete mathematics. The text presents the core of the theory with chapters on unlabelled enumeration and ordinary generating func...

Fostering Recursive Thinking in Combinatorics through the Use of Manipulatives and Computing Technology

Anne Pieper currently teaches high school geometry at The Westminster Schools in Atlanta, Georgia. She recently graduated fromThe University of Georgia with an M.A. in Mathematics Education. Current trends in the revision of both mathematics curricula and traditional teaching strategies include the incorporation of discrete mathematics into the secondary school curriculum (Dossey, 1990). Seriou...