Sharp Upper and Lower Bounds on the Length of General Davenport-Schinzel
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.75
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book investigates Davenport-Schinzel sequences, a subject of combinatorial and computational geometry, to provide optimal bounds for the maximal length of general sequences. In doing so, the author generalizes the techniques employed in establishing bounds for 4-element sequences to sequences of higher order. Additionally, the book extends and refines results concerning a class of Davenport-Schinzel sequences developed by the author in previous work. Going beyond the bounds established by previous research, the author presents sharp upper and lower bounds for the length of sequences of order 4. For sequences of higher orders, the author establishes almost tight upper and lower bounds, significantly improving on previously known results, making this a valuable resource for researchers and practitioners alike. 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.…
Seller Inventory # 9781332093717_0
- Title
- Sharp Upper and Lower Bounds on the Length of General Davenport-Schinzel
- Author
- P. Agarwal, M. Sharir
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 133209371X
- ISBN 13
- 9781332093717
- Seller catalogs
- Calculus
This work presents new bounds for Davenport-Schinzel sequences, a key concept in computational geometry. It focuses on how long these sequences can be under various order constraints and what that means for related problems.
The authors generalize techniques to obtain tighter estimates for higher orders, including a detailed look at the order four case and extensions to larger orders. The approach uses decompositions, new function families tied to Ackermann’s function, and a careful inductive framework to bridge gaps between upper and lower bounds. The results highlight how sharp estimates influence the complexity of core geometric problems and related algorithms.
- Understand what Davenport-Schinzel sequences are and why they matter in geometry
- See how sequences can be decomposed into chains to study their length
- Learn about the role of Ackermann-type functions in deriving bounds
- Discover how these bounds translate into practical limits for geometric problems
Ideal for readers of combinatorial geometry, algorithm design, and researchers interested in sequence bounds and their applications.
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Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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