A New Partial Order on Sequences
by
Scott W. Williams
State University of New York at Buffalo

N = the set of non-negative integers. We discuss variants of a new (pre-) partial order on N^N, which has applications/relations to General Topology, Topological Dynamics, Algebra, and coding. Suppose s is a sequence in N, and B is a sequence of finite sequences of in N. Replace each s(n) by B(s(n)) and form, by adjunction, a new sequence s(B) in N. We say that s codes a sequence t if there is a B with t = s(B). We say t < s provided s codes t, but t does not code s. A finer partial order allows shifts of s to code t. A courser partial order requires a bound on the length of the finite sequences B(n). We consider the sizes of equivalence classes (under coding), and the sizes of chains and anti-chains (under <). We consider codes for 0, 1 sequences.

Date received: February 26, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caam-21.