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Alternative formulae for the number of sublattices. (English) Zbl 1188.05010

Summary: Two formulae for the number of sublattices of a given index \(k\) of an \(n\)-dimensional lattice are presented. They are based on the decomposition of the index k into a product of prime numbers and have the form of a rational function of these primes. Compared with other known methods, they can give the result in a much quicker and more comfortable way.

MSC:

05A15 Exact enumeration problems, generating functions
11H06 Lattices and convex bodies (number-theoretic aspects)
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