Cookies?
Library Header Image
LSE Research Online LSE Library Services

Permutation capacities of families of oriented infinite paths

Brightwell, Graham, Cohen, Gerard, Toth, Agnes, Fairthorne, Marianne, Fachini, Emanuela, Koerner, Janos and Simonyi, Gabor (2010) Permutation capacities of families of oriented infinite paths. SIAM Journal on Discrete Mathematics, 24 (2). pp. 441-456. ISSN 0895-4801

Full text not available from this repository.
Identification Number: 10.1137/090765407

Abstract

Korner and Malvenuto asked whether one can find ((n)(left perpendicularn/2right perpendicular)) linear orderings (i.e., permutations) of the first n natural numbers such that any pair of them places two consecutive integers somewhere in the same position. This led to the notion of graph-different permutations. We extend this concept to directed graphs, focusing on orientations of the semi-infinite path whose edges connect consecutive natural numbers. Our main result shows that the maximum number of permutations satisfying all the pair wise conditions associated with all of the various orientations of this path is exponentially smaller, for any single orientation, than the maximum number of those permutations which satisfy the corresponding pairwise relationship. This is in sharp contrast to a result of Gargano, Korner, and Vaccaro concerning the analogous notion of Sperner capacity of families of finite graphs. We improve the exponential lower bound for the original problem and list a number of open questions.

Item Type: Article
Official URL: http://epubs.siam.org/
Additional Information: © 2010 Thomson Reuters
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 05 Aug 2010 10:35
Last Modified: 13 Sep 2024 22:48
Funders: Hungarian Foundation for Scientific Research (OTKA)
URI: http://eprints.lse.ac.uk/id/eprint/28815

Actions (login required)

View Item View Item