Use of a combinatorial identity for the enumeration of combinations invariant with respect to permutation. (Russian. English summary) Zbl 0614.05007

Koganov, L. M.

Čas. Pěstování Mat. 112, 58-65 (1987).

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

Keywords:

combination; combinatorial identity; Stirling double indexed sequence; enumeration