A Combinatorialist Counts the Rational Numbers

Document Type

Presentation Abstract

Presentation Date

9-6-2001

Abstract

We show that there is an (amazing!) integer valued function f(n) (n=0,1,2,...) such that

(a) the sequence f(0)/f(1), f(1)/f(2), f(2)/f(3), ... consists of all of the positive rational numbers, each occurring once and only once, and

(b) f(n) and f(n+1) are always relatively prime, so each rational occurs in part (a) in reduced form, and

(c) the function f(n) actually counts something of combinatorial interest.

Additional Details

This talk is part of The Big Sky Conference, sponsored by the National Science Foundation and the Department of Mathematical Sciences.

Thursday, 6 September 2001
4:10 p.m. in James E Todd Building CE 203-204
Reception at 3:30 p.m. CE 204

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