Vol. 13, No. 5, 2020

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Counting pseudo progressions

Jay Cummings, Quin Darcy, Natalie Hobson, Drew Horton, Keith Rhodewalt, Morgan Throckmorton and Ry Ulmer-Strack

Vol. 13 (2020), No. 5, 759–780
Abstract

An m-pseudo progression is an increasing list of numbers for which there are at most m distinct differences between consecutive terms. This object generalizes the notion of an arithmetic progression. We give two counts for the number of k-term m-pseudo progressions in {1,2,,n}. We also provide computer-generated tables of values which agree with both counts and graphs that display the growth rates of these functions. Finally, we present a generating function which counts k-term progressions in {1,2,,n} whose differences are all distinct, and we discuss further directions in Ramsey theory.

Keywords
enumerative combinatorics, pseudo progressions
Mathematical Subject Classification
Primary: 05A15
Milestones
Received: 7 June 2019
Revised: 24 July 2020
Accepted: 25 August 2020
Published: 5 December 2020

Communicated by Kenneth S. Berenhaut
Authors
Jay Cummings
Department of Mathematics and Statistics
California State University
Sacramento, CA
United States
Quin Darcy
Department of Mathematics and Statistics
California State University
Sacramento, CA
United States
Natalie Hobson
Department of Mathematics and Statistics
Sonoma State University
Rohnert Park, CA
United States
Drew Horton
Department of Mathematics and Statistics
Sonoma State University
Rohnert Park, CA
United States
Keith Rhodewalt
Department of Mathematics and Statistics
Sonoma State University
Rohnert Park, CA
United States
Morgan Throckmorton
Department of Mathematics and Statistics
California State University
Sacramento, CA
United States
Ry Ulmer-Strack
Department of Mathematics and Statistics
California State University
Sacramento, CA
United States