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Abstract: This paper deals with Carlitz compositions of natural numbers (adjacent parts have to be different). The following parameters are analyzed: Number of parts, number of equal adjacent parts in ordinary compositions, largest part, Carlitz compositions with zeros allowed (correcting an erroneous formula from Carlitz). It is also briefly demonstrated that so--called 1--compositions of a natural number can be treated in a similar style. --- October 14, 1997 --- 1. (Update)
Context of citations to this paper: More
...problems become more interesting when constraints relating to the parts a i or their relative order are introduced. For example, in [2] compositions with no two adjacent equal parts are studied, and in [5] compositions with all parts distinct are considered. Binary...
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Compositions With Parts Constrained By The - Leading Summand Arnold (Correct)
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BibTeX entry: (Update)
A. Knopfmacher and H. Prodinger. On Carlitz compositions. European J. of Combinatorics, 19:579-589, 1998. http://citeseer.ist.psu.edu/knopfmacher98carlitz.html More
@misc{ knopfmacher98carlitz,
author = "A. Knopfmacher and H. Prodinger",
title = "On Carlitz compositions",
text = "A. Knopfmacher and H. Prodinger. On Carlitz compositions. European J. of
Combinatorics, 19:579-589, 1998.",
year = "1998",
url = "citeseer.ist.psu.edu/knopfmacher98carlitz.html" }
Citations (may not include all citations):154 Combinatorial Enumeration (context) - Goulden, Jackson - 1983
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105 The Encyclopedia of Integer Sequences (context) - Sloane, Plouffe - 1995
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10 The Average Time for Carry Propagation (context) - Knuth - 1978
9 Algorithmique et G'eom'etrie des Polynomes (context) - Gourdon - 1996
8 Level Number Sequences for Trees (context) - Flajolet, Prodinger - 1987
6 Measures of Distinctness for Random Partitions and Compositi.. - Hwang, Yeh - 1997
6 Compositions with m distinct parts - Knopfmacher, Mays
5 The hard-hexagon model and Rogers--Ramanujan type identities (context) - Andrews - 1981
4 Restricted Compositions (context) - Carlitz - 1976
4 American Mathematical Monthly (context) - Odlyzko, Wilf et al. - 1978
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