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On the discrepancy of 3 permutations
Author(s) -
Bohus Géza
Publication year - 1990
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.3240010208
Subject(s) - hypergraph , combinatorics , mathematics , conjecture , bounded function , element (criminal law) , constant (computer programming) , set (abstract data type) , discrete mathematics , computer science , mathematical analysis , political science , law , programming language
Abstract Consider different orderings of an n ‐element set and the hypergraph consisting of the intervals of these orderings. A conjecture of J. Beck states that in the case of three orderings this hypergraph has bounded discrepancy. We show that for any constant number of orderings the discrepancy is O (log n ). the proof also gives an efficient algorithm to determine such a coloring.