On the number and sizes of double cosets of Sylow subgroups of the symmetric group

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • Persi Diaconis
  • Eugenio Giannelli
  • Robert M. Guralnick
  • Stacey Law
  • Gabriel Navarro
  • Benjamin Sambale
  • Hunter Spink

Organisationseinheiten

Externe Organisationen

  • Stanford University
  • Università degli Studi di Firenze (UniFi)
  • University of Southern California (USC)
  • University of Birmingham
  • Universitat de Valencia
  • University of Toronto
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Details

OriginalspracheEnglisch
Seiten (von - bis)62-86
Seitenumfang25
FachzeitschriftJournal of algebra
Jahrgang689
Frühes Online-Datum24 Okt. 2025
PublikationsstatusVeröffentlicht - 1 März 2026

Abstract

Let Pn be a Sylow p-subgroup of the symmetric group Sn. We investigate the number and sizes of the Pn∖Sn/Pn double cosets, showing that ‘most’ double cosets have maximal size when p is odd, or equivalently, that Pn∩Pnx=1 for most x∈Sn when n is large. We also find that all possible sizes of such double cosets occur, modulo a list of small exceptions.

ASJC Scopus Sachgebiete

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On the number and sizes of double cosets of Sylow subgroups of the symmetric group. / Diaconis, Persi; Giannelli, Eugenio; Guralnick, Robert M. et al.
in: Journal of algebra, Jahrgang 689, 01.03.2026, S. 62-86.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Diaconis, P, Giannelli, E, Guralnick, RM, Law, S, Navarro, G, Sambale, B & Spink, H 2026, 'On the number and sizes of double cosets of Sylow subgroups of the symmetric group', Journal of algebra, Jg. 689, S. 62-86. https://doi.org/10.1016/j.jalgebra.2025.09.036
Diaconis, P., Giannelli, E., Guralnick, R. M., Law, S., Navarro, G., Sambale, B., & Spink, H. (2026). On the number and sizes of double cosets of Sylow subgroups of the symmetric group. Journal of algebra, 689, 62-86. https://doi.org/10.1016/j.jalgebra.2025.09.036
Diaconis P, Giannelli E, Guralnick RM, Law S, Navarro G, Sambale B et al. On the number and sizes of double cosets of Sylow subgroups of the symmetric group. Journal of algebra. 2026 Mär 1;689:62-86. Epub 2025 Okt 24. doi: 10.1016/j.jalgebra.2025.09.036
Diaconis, Persi ; Giannelli, Eugenio ; Guralnick, Robert M. et al. / On the number and sizes of double cosets of Sylow subgroups of the symmetric group. in: Journal of algebra. 2026 ; Jahrgang 689. S. 62-86.
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AU - Diaconis, Persi

AU - Giannelli, Eugenio

AU - Guralnick, Robert M.

AU - Law, Stacey

AU - Navarro, Gabriel

AU - Sambale, Benjamin

AU - Spink, Hunter

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