Geodesic
Integral representation and the computation of multiple combinatorial sums from Hall's commutator theory
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 1, pp. 12-20.

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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
Mots-clés : P. Hall's collection formula. 
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Georgy P. Egorychev; Sergey G. Kolesnikov; Vladimir M. Leontiev. Integral representation and the computation of multiple combinatorial sums from Hall's commutator theory. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 1, pp. 12-20. http://geodesic.mathdoc.fr/item/JSFU_2021_14_1_a1/

[1] P. Hall, “A contribution to the theory of groups of prime-power order”, Proc. London Math. Soc., 36:2 (1934), 29–95

[2] M. Hall, Jr., The Theory of Groups, Macmillian, New York, 1959

[3] E.F. Krause, “On the collection process”, Proc. Amer. Math. Soc., 15 (1964), 497–504

[4] A.I. Skopin, “The Jacobi identity and P. Hall's collection formula for transmetabelian groups of two types”, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 175, 1989, 106–112 (in Russian)

[5] V.M. Leontiev, “Combinatorial problems connected with P. Hall's collection process”, Siberian Electronic Mathematical Reports, 17 (2020), 873–889 (in Russian)

[6] S. Kolesnikov, V. Leontiev, G. Egorychev, “Two collection formulas”, Journal of Group Theory, 23:4 (2020), 607–628 | DOI

[7] G.P. Egorychev, Integral Representation and the Computation of Combinatorial Sums, Nauka, Novosibirsk, 1977 (in Russian); Mathematical Monographs, American Mathematical Society, 1984; 2nd ed., 1989

[8] M.R. Riedel, Egorychev method and the evaluation of binomial coefficient sums, , 2020 http://pnp.mathematik.uni-stuttgart.de/iadm/Riedel/papers/egorychev.pdf

[9] G.P. Egorychev, Yu.M. Gorchakov, “The ranks of the factors in the lower central series of a free polynilpotent group”, Dokl. Akad. Nauk SSSR, 204 (1972), 12–14

[10] V.M. Leontiev, “On Divisibility of Some Sums of Binomial Coefficients Arising From Collection Formulas”, Journal of Siberian Federal University. Mathematics $\$ Physics, 11:5 (2018), 603–614 | DOI