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Use of a combinatorial identity for the enumeration of combinations invariant with respect to permutation. (Russian. English summary) Zbl 0614.05007
A general definition of combination is introduced. It is proved that formulas of A. Vrba concerning the fundamental matrix functions as well as Manning’s lemma from symbolic dynamics are consequences of a generally known combinatorial identity which serves (with necessary appendix) for complete determination of Stirling double indexed sequence of 2nd kind. The proofs are based on the enumeration of combinations invariant with respect to a fixed substitution with a given number of cycles.
##### MSC:
 05A19 Combinatorial identities, bijective combinatorics 05A15 Exact enumeration problems, generating functions
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