By Micha Sharir
Functions of Davenport-Schinzel sequences come up in components as diversified as robotic movement making plans, special effects and imaginative and prescient, and development matching. those sequences convey a few outstanding homes that cause them to a desirable topic for examine in combinatorial research. This ebook offers a finished learn of the combinatorial houses of Davenport-Schinzel sequences and their quite a few geometric purposes. those sequences are refined instruments for fixing difficulties in computational and combinatorial geometry. this primary e-book at the topic through of its major researchers should be an incredible source for college kids and execs in combinatorics, computational geometry, and similar fields.
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Extra resources for Davenport-Schinzel Sequences and their Geometric Applications
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254). 15) σ−1 (n) + two trivial terms. 16) n=1 ∞ = K a2 n=1 Proof. 15). 1), we find that ∞ 0 (e2π x dx = − 1)(e2πa/x − 1) ∞ ∞ m=1 k=1 ∞ 1 m σ−1 (n) = n=1 √ =2 a ∞ ∞ e−2π(u+akm/u) du 0 ∞ e−2π(u+an/u) du 0 √ √ σ−1 (n) n K 1 (4π an ). 16) giving the identities of the missing terms. 34 Bruce C. 5 (p. 254). If a > 0 and γ denotes Euler’s constant, then ∞ √ 2 a √ √ σ−1 (n) n K 1 (4π an ) n=1 =− a2 2π + ∞ n=1 σ−1 (n) a + ((log a + γ )ζ (2) + ζ (2)) n(n + a) 2π 1 1 (log 2aπ + γ ) + . 17) Proof. 10), set α = x, so that β = π 2 /x.