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A "Challenging Question" of Björner from 1976: Every Infinite Geometric Lattice of Finite Rank Has a Matching

It is proven that every geometric lattice of finite rank greater than 1 has a matching between the points and hyperplanes. This answers a question of Pólya Prize-winner Anders Björner from the 1981 Banff Conference on Ordered Sets, which he raised as a "challenging question" in 1976.

preprint2020arXivOpen access
Jonathan David Farley
math.CO
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Jonathan David Farley

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