an:03993593
Zbl 0614.05007
Koganov, L. M.
Use of a combinatorial identity for the enumeration of combinations invariant with respect to permutation
RU
??as. P??stov??n?? Mat. 112, 58-65 (1987).
00178756
1987
j
05A19 05A15
combination; combinatorial identity; Stirling double indexed sequence; enumeration
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.