Nonlinearity of Davenport-Schinzel Sequences and of a Generalized Path Compression Scheme
نویسندگان
چکیده
Davenport-Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in the computation of the envelope of a set of functions. We show that the maximal length of a Davenport-Schinzel sequence composed of n symbols is 6(noc(n»), where t1.(n)is the functional inverse of Ackermann's function, and is thus very slowly increasing to infinity. This is achieved by establishing an equivalence between such sequences and generalized path compression schemes on rooted trees, and then by analyzing these schemes.
منابع مشابه
Keywords. Davenport{schinzel Sequence; Tree; Extremal Problem 0 Extremal Problems for Colored Trees and Davenport{schinzel Sequences
In the theory of generalized Davenport{Schinzel sequences one estimates the maximum lengths of nite 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 mo...
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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 ...
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Article history: Received 8 August 2010 Available online xxxx
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عنوان ژورنال:
- Combinatorica
دوره 6 شماره
صفحات -
تاریخ انتشار 1984