Sunday, July 30, 2017

Baskets have A-trails!

Bridges Waterloo 2017 was great. Thanks to the organizers and Craig Kaplan especially.

I am posting a pdf of my presentation on google drive.

Baskets have A-trails!

Too late to include in my talk, I learned of Anton Kotzig's proof from the 1960's that every genus zero 4-regular map has an A-trail. Wow. Given any map on the sphere, the map operation Medial (which also gives the path of the weavers) converts it into a map with an A-trail. It follows that the weaver pattern (not the weaving) can be constructed by pinching an untwisted loop (like the kids were doing in todays Family Day activity.) By the way, great work guys.

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