Journal of Integer Sequences, Vol. 12 (2009), Article 09.3.3

Combinatorial Interpretation of Generalized Stirling Numbers


Wolfdieter Lang
Institut für Theoretische Physik
Universität Karlsruhe
D-76128 Karlsruhe
Germany

Abstract:

A combinatorial interpretation of the earlier studied generalized Stirling numbers, emerging in a normal ordering problem and its inversion, is given. It involves unordered forests of certain types of labeled trees. Partition number arrays related to such forests are also presented.

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(Concerned with sequences A000108 A000142 A000169 A000369 A001710 A001764 A002293 A002294 A002295 A002296 A007556 A008287 A008297 A008545 A023531 A035342 A036039 A036040 A002293 A049352 A062994 A107106 A130561 A134133 A134134 A134144 A134145 A134146 A134149 A134150 A134151 A134273 A134274 A134275 A134278 A134279 A134280 A134286 A143171 A143172 A143173 A144267 A144268 A144269 A144270 A144274 A144275 A144279 A144280 A144284 A144285 A144341 A144342 A144351 A144353 A144354 A144355 A144356 A144357 A144358 A144877 A144878 A144879 A144880 A144881 A144885 A144886 A144890 A144891 A145356 A145357 A145361 A145362 A145363 A145364 A145367 A145369 A145370 A145372 and A145373.)

Received October 16 2008; revised version received March 6 2009. Published in Journal of Integer Sequences, March 14 2009.

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