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Orbits of
finite-field hypergeometric functions and complete subgraphs
of generalized Paley graphs
Dermot McCarthy and Mason Springfield |
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Vol. 17 (2024), No. 2, 355–362
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Abstract |
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In a recent result of Dawsey and McCarthy, a formula for the number of complete subgraphs of order 4 of generalized Paley graphs is given in terms of a sum of finite-field hypergeometric functions. Via known transformation formulas for finite-field hypergeometric functions, many of the summands in their formula are equal. They construct a group action representing these transformations so that the number of summands that need to be evaluated is reduced to orbit representatives. We expand the group used by Dawsey and McCarthy, reducing by up to 80% the number of summands to be evaluated. |
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Keywords
hypergeometric functions, finite-field hypergeometric
functions, Paley graphs
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Mathematical Subject Classification
Primary: 11T24, 05C25
Secondary: 05C30, 33C99
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Supplementary material |
Milestones
Received: 26 September 2023
Revised: 20 February 2024
Accepted: 21 February 2024
Published: 20 May 2024
Communicated by Kenneth S. Berenhaut
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Authors |
| Dermot McCarthy | |
| Department of Mathematics &
Statistics Texas Tech University Lubbock, TX United States |
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| Mason Springfield | |
| Department of Mathematics &
Statistics Texas Tech University Lubbock, TX United States |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
