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On the gap structure of sequences of points on a circle

✍ Scribed by Lyle Ramshaw

Publisher
Elsevier Science
Year
1978
Weight
831 KB
Volume
81
Category
Article
ISSN
1385-7258

No coin nor oath required. For personal study only.

✦ Synopsis

Considerable mathematical effort h as gone in t o studying seq uences of points in t.he interval [0, I) which are even ly di stributed, in the se ns e that cer t a in interval s contain rou ghl y the correct percentages of t he first n points. This paper ex plores the related notion in which a sequen ce is even ly di stributed if its first n points split a give n circle into intervals which a re roughl y eq ual in len gth, regardless of their relative po sitions. The sequenc e Xk= (l Og 2 (2k-l) m od 1) was introduced in t h is context by D e Bruijn and E rd os . W e w ill see that tho gap struct u re of this seque nce is uniquely optimal in It certai n sens e, and op timal undo r a wide clas s of m easures .

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