Predicates whose maximal length functions increase periodically
Document Type
Article
Publication Date
8-15-1990
Department
Department of Mathematical Sciences
Abstract
Let P be a predicate defined on finite sets of positive integers and define LP(n) to be the Largest cardinality of subsets of {1, 2, ..., n} for which P is false. We exhibit conditions on P which force the existence of integers N, M, and K so that LP(n + M) = LP(n) + K whenever n> N. For such predicates we say that LP increases periodically. In particular, we show that if D is a finite set of tuples of positive integers, then LP increases periodically for the predicate P="X contains as s-tuple {ai}s1 with {ai + 1 - ai}s - 11 in D". This extends the main result in [2], as well as results of Erdo{combining double acute accent}s, Hemminger and McKay, Liu, and Wagstaff.
Publication Title
Discrete Mathematics
Recommended Citation
Gilpin, M.,
&
Shelton, R.
(1990).
Predicates whose maximal length functions increase periodically.
Discrete Mathematics,
84(1), 15-21.
http://doi.org/10.1016/0012-365X(90)90268-M
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5240