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26

DM
1998

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On numbers of Davenport-Schinzel sequences

13 years 10 months ago

On numbers of Davenport-Schinzel sequences

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One class of Davenport-Schinzel sequences consists of ﬁnite sequences over n symbols without immediate repetitions and without any subsequence of the type abab. We present a bijective encoding of such sequences by rooted plane trees with distinguished nonleaves and we give a combinatorial proof of the formula 1 k − n + 1 2k − 2n k − n k − 1 2n − k − 1 for the number of such normalized sequences of length k. The formula was found by Gardy and Gouyou-Beauchamps by means of generating functions. We survey previous results concerning counting of DS sequences and mention several equivalent enumerative problems.

Martin Klazar

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Davenport-Schinzel Sequences | DM 1998 | Sequences | ﬁnite Sequences |

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Added	22 Dec 2010
Updated	22 Dec 2010
Type	Journal
Year	1998
Where	DM
Authors	Martin Klazar

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