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 J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 1, Pages 12–20 (Mi jsfu886)

Integral representation and the computation of multiple combinatorial sums from Hall's commutator theory

Georgy P. Egorychev, Sergey G. Kolesnikov, Vladimir M. Leontiev

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: In this paper we prove a series of combinatorial identities arising from computing the exponents of the commutators in P. Hall's collection formula. We also compute a sum in closed form that arises from using the collection formula in Chevalley groups for solving B. A. F. Wehrfritz problem on the regularity of their Sylow subgroups.

Keywords: integral representation, method of coefficients, P. Hall's collection formula.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1534/1 This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement no. 075-02-2020-1534/1).

DOI: https://doi.org/10.17516/1997-1397-2021-14-1-12-20

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UDC: 519.1+517.44+512.54
Accepted: 20.11.2020
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Citation: Georgy P. Egorychev, Sergey G. Kolesnikov, Vladimir M. Leontiev, “Integral representation and the computation of multiple combinatorial sums from Hall's commutator theory”, J. Sib. Fed. Univ. Math. Phys., 14:1 (2021), 12–20

Citation in format AMSBIB
\Bibitem{EgoKolLeo21} \by Georgy~P.~Egorychev, Sergey~G.~Kolesnikov, Vladimir~M.~Leontiev \paper Integral representation and the computation of multiple combinatorial sums from Hall's commutator theory \jour J. Sib. Fed. Univ. Math. Phys. \yr 2021 \vol 14 \issue 1 \pages 12--20 \mathnet{http://mi.mathnet.ru/jsfu886} \crossref{https://doi.org/10.17516/1997-1397-2021-14-1-12-20} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000615268200002}