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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
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Abstract |
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An -pseudo progression is an increasing list of numbers for which there are at most distinct differences between consecutive terms. This object generalizes the notion of an arithmetic progression. We give two counts for the number of -term -pseudo progressions in . 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 -term progressions in whose differences are all distinct, and we discuss further directions in Ramsey theory. |
Keywords
enumerative combinatorics, pseudo progressions
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Mathematical Subject Classification
Primary: 05A15
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Milestones
Received: 7 June 2019
Revised: 24 July 2020
Accepted: 25 August 2020
Published: 5 December 2020
Communicated by Kenneth S. Berenhaut
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Authors |
| Jay Cummings | |
| Department of Mathematics and
Statistics California State University Sacramento, CA United States |
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| Quin Darcy | |
| Department of Mathematics and
Statistics California State University Sacramento, CA United States |
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| Natalie Hobson | |
| Department of Mathematics and
Statistics Sonoma State University Rohnert Park, CA United States |
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| Drew Horton | |
| Department of Mathematics and
Statistics Sonoma State University Rohnert Park, CA United States |
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| Keith Rhodewalt | |
| Department of Mathematics and
Statistics Sonoma State University Rohnert Park, CA United States |
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| Morgan Throckmorton | |
| Department of Mathematics and
Statistics California State University Sacramento, CA United States |
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| Ry Ulmer-Strack | |
| Department of Mathematics and
Statistics California State University Sacramento, CA United States |
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