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math.CO2020
Another Problem of Jónsson and McKenzie from 1982: Refinement Properties for Connected Powers of Posets
Jonathan David Farley
In 1982, Jónsson and McKenzie posed the following problem: "Find counter examples (or prove that none exist) to the refinement of [, , , and non-empty p…
math.CO2020★ 2 cited
An Issue Raised in 1978 by a Then-Future Editor-in-Chief of the Journal "Order": Does the Endomorphism Poset of a Finite Connected Poset Tell Us That the Poset Is Connected?
Jonathan David Farley
In 1978, Dwight Duffus---editor-in-chief of the journal "Order" from 2010 to 2018 and chair of the Mathematics Department at Emory University from 1991 to 2005---wrote that "it is…
math.CO2020
A "Challenging Question" of Björner from 1976: Every Infinite Geometric Lattice of Finite Rank Has a Matching
Jonathan David Farley
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 Björ…