Counting pseudo progressions

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

doi:10.2140/involve.2020.13.759

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-4184 (e-only)

ISSN: 1944-4176 (print)

Author Index

Coming Soon

Other MSP Journals

This article is available for purchase or by subscription. See below.

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

DOI: 10.2140/involve.2020.13.759

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 ${1, 2, \dots, n}$ . 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 ${1, 2, \dots, n}$ whose differences are all distinct, and we discuss further directions in Ramsey theory.

PDF Access Denied

We have not been able to recognize your IP address 18.223.151.18 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

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

Vol. 13, No. 5, 2020