A proof-heavy, open-access graduate textbook on algebraic combinatorics, including a full proof of the Littlewood-Richardson rule.
Projective geometry over F_1 and the Gaussian binomial coefficients
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abstract
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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An Introduction to Algebraic Combinatorics
A proof-heavy, open-access graduate textbook on algebraic combinatorics, including a full proof of the Littlewood-Richardson rule.