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Projective geometry over F_1 and the Gaussian binomial coefficients

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arxiv math/0407093 v1 pith:M6DVRI5F submitted 2004-07-07 math.CO

Henry Cohn This is my paper · ORCID
classification math.CO
keywords binomialcoefficientsfieldgaussiangeometrynotionprojectivethere
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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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Cited by 1 Pith paper

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  1. An Introduction to Algebraic Combinatorics

    math.CO 2025-05 conditional novelty 2.0 of 10

    A proof-heavy, open-access graduate textbook on algebraic combinatorics, including a full proof of the Littlewood-Richardson rule.

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