#### Author:

William T. Trotter

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#### Category:

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#### ePub size:

1848 kb

#### Other formats:

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#### Rating:

4.6

#### Publisher:

Johns Hopkins University Press (January 1, 2002)

#### Pages:

328

#### ISBN:

0801869773

# Combinatorics and Partially Ordered Sets: Dimension Theory (Johns Hopkins Studies in the Mathematical Sciences) e-book

#### by William T. Trotter

William T. Trotter is Regents' Professor of Mathematics at Arizona State University and director of Combinatorics and . Series: Johns Hopkins Studies in the Mathematical Sciences (Book 6).

Series: Johns Hopkins Studies in the Mathematical Sciences (Book 6).

By William T. Trotter.

By William T. Johns Hopkins University Press.

Book Description The Johns Hopkins University Press.

Trotter, Prof William T. Published by The Johns Hopkins University Press. Book Description The Johns Hopkins University Press.

Published in Contemporary Trends in Discrete Mathematics 1997.

Streib . In: Bárány . Solymosi . Sági G. (eds) An Irregular Mind.

Johns Hopkins University Press, Baltimore, MD, 1992. Streib . Bolyai Society Mathematical Studies, vol 21. Springer, Berlin, Heidelberg.

Dimension theory, Johns Hopkins Series in the Mathematical Sciences

Johns Hopkins University Press, Baltimore, 1992, Vinokurov in Soviet Math Dokl 168(3):663–666, 1966, Zhang et al. in Discr Math 340(5):1086–1091, 2017). Dimension theory, Johns Hopkins Series in the Mathematical Sciences. We prove that there exists no polynomial-time algorithm to approximate the dimension of a poset on N elements with a factor of O(N. −ϵ) for any ϵ 0, unless NP ZPP.

linear extensions Li, Lj in the LINEAR EXTENSION DIAMETER problem

linear extensions Li, Lj in the LINEAR EXTENSION DIAMETER problem. The Johns Hopkins University Press, Baltimore, MD, 1992. ISBN 0-8018-4425- 8. Johns Hopkins Series in the Mathematical Sciences

By William T. Johns Hopkins Series in the Mathematical Sciences.

Primarily intended for research mathematicians and computer scientists, *Combinatorics and Partially Ordered Sets: Dimension Theory* also serves as a useful text for advanced students in either field. William Trotter concentrates on combinatorial topics for finite partially ordered sets, and with dimension theory serving as a unifying theme, research on partially ordered sets or posets is linked to more traditional topics in combinatorial mathematics―including graph theory, Ramsey theory, probabilistic methods, hypergraphs, algorithms, and computational geometry. The book's most important contribution is to collect, organize, and explain the many theorems on partially ordered sets in a way that makes them available to the widest possible audience.

Chapters: Introduction to Dimension • Crowns, Splits, Stacks, Sums and Products • Characterization Problems for Posets, Lattices, Graphs, and Families of Sets • Hypergraph Coloring, Computational Complexity, and Irreducible Posets • Planar Posets and Trees • Planar Graphs, Planar Maps and Convex Polytopes • Probabilistic Methods in Dimension Theory • Interval and Geometric Containment Orders • Greedy Dimension, Back-Tracking, and Depth First Search • Products of Chains of Bounded Length • Large Minimal Realizers