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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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.

 

Ideal solutions in the Prouhet–Tarry–Escott problem
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by Don Coppersmith, Michael J. Mossinghoff, Danny Scheinerman and Jeffrey M. VanderKam;
Math. Comp. 93 (2024), 2473-2501
DOI: https://doi.org/10.1090/mcom/3917
Published electronically: November 6, 2023

Abstract:

For given positive integers $m$ and $n$ with $m<n$, the Prouhet–Tarry–Escott problem asks if there exist two disjoint multisets of integers of size $n$ having identical $k$th moments for $1\leq k\leq m$; in the ideal case one requires $m=n-1$, which is maximal. We describe some searches for ideal solutions to the Prouhet–Tarry–Escott problem, especially solutions possessing a particular symmetry, both over $\mathbb {Z}$ and over the ring of integers of several imaginary quadratic number fields. Over $\mathbb {Z}$, we significantly extend searches for symmetric ideal solutions at sizes $9$, $10$, $11$, and $12$, and we conduct extensive searches for the first time at larger sizes up to $16$. For the quadratic number field case, we find new ideal solutions of sizes $10$ and $12$ in the Gaussian integers, of size $9$ in $\mathbb {Z}[i\sqrt {2}]$, and of sizes $9$ and $12$ in the Eisenstein integers.
References
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Bibliographic Information
  • Don Coppersmith
  • Affiliation: Center for Communications Research, Princeton, New Jersey
  • MR Author ID: 51455
  • Email: dcopper@idaccr.org
  • Michael J. Mossinghoff
  • Affiliation: Center for Communications Research, Princeton, New Jersey
  • MR Author ID: 630072
  • ORCID: 0000-0002-7983-5427
  • Email: m.mossinghoff@idaccr.org
  • Danny Scheinerman
  • Affiliation: Center for Communications Research, Princeton, New Jersey
  • ORCID: 0000-0002-3985-325X
  • Email: daniel.scheinerman@gmail.com
  • Jeffrey M. VanderKam
  • Affiliation: Center for Communications Research, Princeton, New Jersey
  • MR Author ID: 606412
  • Email: vanderkm@idaccr.org
  • Received by editor(s): April 21, 2023
  • Received by editor(s) in revised form: August 12, 2023, and September 20, 2023
  • Published electronically: November 6, 2023
  • Additional Notes: This work is dedicated to the memory of Peter Borwein.
    The second author is the corresponding author
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 93 (2024), 2473-2501
  • MSC (2020): Primary 11D72, 11Y50; Secondary 11D79, 11P05, 11R11
  • DOI: https://doi.org/10.1090/mcom/3917
  • MathSciNet review: 4759381