Cute proof of Sperner's theorem (https://en.wikipedia.org/wiki/Sperner%27s_theorem) from a talk by R. P. Stanley last Thursday: represent subsets of \([0,n-1]\) by strings of \(n\) parens, ")" in position \(i\) if \(i\) is in the set, "(" otherwise. In each string, flip the first unmatched (, grouping the subsets into chains like (()(( – )()(( – )())( — )())). Each chain touches the middle level once, and any other antichain at most once, so the middle level is the biggest antichain. #proofinatoot

I made a new page of sliding block puzzles:

http://homepages.gac.edu/~jsiehler/games/blocks-start.html

Some great mathematical "colemanballs"

Quit using Mendeley people!

They started encrypting your database so you cannot easily move it over to other tools any more.

See:

https://www.zotero.org/support/kb/mendeley_import

That link also helps you saving your data before it's too late.

(Elsevier are a bunch of crooks, blocking interoperability one-way and not the other. Almost as bad as Google blocking uBlock for your safety...)

Recently, Bekos et al made a major breakthrough, showing that planar graphs of bounded degree have bounded queue number.

https://arxiv.org/abs/1811.00816

We were able to generalize this to bounded degree bounded genus graphs.

https://en.wikipedia.org/wiki/Grete_Hermann

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