All binomial identities are orderable

March 29, 2016 ยท The Ethereal ยท ๐Ÿ› European journal of combinatorics (Print)

๐Ÿ”ฎ THE ETHEREAL: The Ethereal
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Authors Dmitry N. Kozlov arXiv ID 1603.08743 Category cs.DM: Discrete Mathematics Cross-listed cs.DC, math.CO Citations 5 Venue European journal of combinatorics (Print) Last Checked 2 months ago
Abstract
The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on the round complexity of the weak symmetry breaking task. Furthermore, we introduce the notion of a fundamental binomial identity and find an infinite family of values, other than the prime powers, for which no fundamental binomial identity can exist.
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