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Robotics Research Technical Report: Planar Realizations of Nonlinear Davenport-Schinzel Sequences by Segments (Classic Reprint) - Brossura

 
9781332178704: Robotics Research Technical Report: Planar Realizations of Nonlinear Davenport-Schinzel Sequences by Segments (Classic Reprint)

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Excerpt from Robotics Research Technical Report: Planar Realizations of Nonlinear Davenport-Schinzel Sequences by Segments

Since the construction in [hs] is not explicit but rather defined in terms of generalized path compressions on trees, we first provide in Section 2 an explicit inductive construction of the sequences of [hs] and analyze their structure (a similar construction has recently been obtained by Komjath Section 3 then proceeds to describe the inductive realization of these sequences by collections of segments.

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9780332360027: Robotics Research Technical Report: Planar Realizations of Nonlinear Davenport-Schinzel Sequences by Segments (Classic Reprint)

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ISBN 10:  0332360024 ISBN 13:  9780332360027
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Ady Wiernik, Micha Sharir
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ISBN 10: 1332178707 ISBN 13: 9781332178704
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Paperback. Condizione: New. Print on Demand. This book presents a construction for realizing nonlinear Davenport-Schinzel sequences by segments. The Davenport-Schinzel sequence, introduced by H. Davenport and A. Schinzel, is a sequence of symbols in which no two adjacent symbols are equal, and it contains no subsequence of the form . Davenport and Schinzel proved that for any natural number, there exists a Davenport-Schinzel sequence of length that uses symbols. In this book, the author constructs a set of segments in the plane whose lower envelope (the pointwise minimum of the segments when viewed as functions of x) consists of subsegments of the segments in the set. The author shows that for each and sufficiently large, there exists a Davenport-Schinzel sequence of length that can be realized by a set of segments. This result settles an open problem in the theory of Davenport-Schinzel sequences and provides a new tool for studying the combinatorial properties of these sequences. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781332178704_0

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