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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Derangements and the $p$-adic incomplete gamma function
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by Andrew O’Desky and David Harry Richman HTML | PDF
Trans. Amer. Math. Soc. 376 (2023), 1065-1087


We introduce a $p$-adic analogue of the incomplete gamma function. We also introduce quantities ($m$-values) associated to a function on natural numbers and prove a new characterization of $p$-adic continuity for functions with $p$-integral $m$-values. Combinatorial interpretations for the integral values of the incomplete gamma function and functions with $m$-values zero or one are obtained, which show that these functions count derangements in generalized symmetric groups and permutations with restricted cycle lengths.
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Additional Information
  • Andrew O’Desky
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey
  • MR Author ID: 1289808
  • ORCID: 0000-0003-1068-7013
  • Email:
  • David Harry Richman
  • Affiliation: Department of Mathematics, University of Washington, Seattle, Washington
  • MR Author ID: 1194208
  • ORCID: 0000-0002-0101-0521
  • Email:
  • Received by editor(s): April 13, 2021
  • Received by editor(s) in revised form: January 15, 2022, March 8, 2022, and March 16, 2022
  • Published electronically: December 1, 2022
  • © Copyright 2022 by the authors
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 1065-1087
  • MSC (2020): Primary 33B20, 11S80, 11B75, 05A05
  • DOI:
  • MathSciNet review: 4531669