On numbers of Davenport-Schinzel sequences

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.

• Type: Journal
• Year: 1998
• Where: DM
• Authors: Martin Klazar
• Keywords: Davenport-Schinzel Sequences, DM 1998, Sequences, finite Sequences