The foundations of enumeration theory for finite nilpotent groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 174-183
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This paper is the first in a series of papers that lay the foundations of enumeration theory for finite groups including the classical inversion calculus on segments of the natural series and on lattices of subsets of finite sets. Since it became possible to calculate the Möbius function on all subgroups of finite nilpotent groups, the Möbius inversion on these groups began to play a decisive role. The efficiency of the inversion method as a regular technique suitable for solution of enumeration problems of group theory is illustrated with a number of concrete and very important enumerations. Bibliography: 13 titles.
@article{ZNSL_1994_211_a15,
author = {V. N. Shokuev},
title = {The foundations of enumeration theory for finite nilpotent groups},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {174--183},
publisher = {mathdoc},
volume = {211},
year = {1994},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a15/}
}
V. N. Shokuev. The foundations of enumeration theory for finite nilpotent groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 174-183. http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a15/