Three Generalizations of Davenport-Schinzel Sequences
نویسنده
چکیده
We present new, and mostly sharp, bounds on the maximum length of certain generalizations of Davenport-Schinzel sequences. Among the results are sharp bounds on order-s double DS sequences, for all s, sharp bounds on sequences avoiding catenated permutations (aka formation free sequences), and new lower bounds on sequences avoiding zig-zagging patterns.
منابع مشابه
Generalized Davenport–Schinzel sequences: results, problems, and applications
We survey in detail extremal results on Davenport–Schinzel sequences and their generalizations, from the seminal papers of H. Davenport and A. Schinzel in 1965 to present. We discuss geometric and enumerative applications, generalizations to colored trees, and generalizations to hypergraphs. Eleven illustrative examples with proofs are given and nineteen open problems are posed.
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In the theory of generalized Davenport–Schinzel sequences one estimates the maximum lengths of finite sequences containing no subsequence of a given pattern. Here we investigate a further generalization, in which the class of sequences is extended to the class of colored trees. We determine exactly the extremal functions associated with the properly 2-colored path of four vertices and with the ...
متن کامل8. Davenport-schinzel Sequences
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 29 شماره
صفحات -
تاریخ انتشار 2015