Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.3

On the Enumeration of Restricted Words over a Finite Alphabet

Daniel Birmajer
Department of Mathematics
Nazareth College
Rochester, NY 14618

Juan B. Gil and Michael D. Weiner
Department of Mathematics and Statistics
Penn State Altoona
Altoona, PA 16601


We present a method for the enumeration of restricted words over a finite alphabet. Restrictions are described through the inclusion or exclusion of suitable building blocks used to construct the words by concatenation. Our approach, which relies on the invert transform and its representation in terms of partial Bell polynomials, allows us to generalize and address in a systematic manner previous results in the subject.

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(Concerned with sequences A000045 A000073 A000078 A000129 A000322 A000930 A001076 A001090 A001109 A001333 A001353 A001906 A003229 A003269 A003520 A004187 A004189 A004190 A004191 A004254 A005251 A005668 A005708 A005709 A005710 A006190 A018913 A028859 A041025 A041041 A049856 A052529 A052918 A052942 A054413 A055099 A055991 A068921 A079675 A084386 A086347 A089977 A099242 A099253 A099371 A108758 A119826 A120925 A123347 A125145 A143447 A143454 A143455 A180033 A180035 A200676 A209239 A255115 A255116 A255117 A255118 A255119 A255813 A255814 A255815.)

Received September 7 2015; revised version received November 22 2015. Published in Journal of Integer Sequences, December 17 2015. Minor revision, January 4 2016.

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