Projective geometry over F_1 and the Gaussian binomial coefficients

Details Projective geometry over F_1 and the Gaussian binomial coefficients Projective geometry over F_1 and the Gaussian binomial coefficients

2004-07-07

arxiv.org/abs/math/0407093v1

American Mathematical Monthly 111 (2004), 487-495

Mathematics

Combinatorics

9 pages

Scientific paper

There is no field with only one element, yet there is a well-defined notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and algebra, but it is rarely discussed as such. The purpose of this article is to bring it to the attention of a broader audience, as the solution to a puzzle about Gaussian binomial coefficients.

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