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SUMMARY:A new proof of the lattice property of the Tamari order - Noam Zei
 lberger (University of Birmingham)
DTSTART:20190205T141500Z
DTEND:20190205T151500Z
UID:TALK117853@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:The so-called "Tamari order" is the partial ordering on\nfully
 -bracketed words induced by a "semi-associative" law (ab)c <=\na(bc).  Amo
 ng its many remarkable properties\, the order induces a\nlattice structure
  on the bracketings of a given word (known as the\n"Tamari lattice"\, or t
 he "rotation lattice of binary trees")\, a\nnon-obvious fact that was firs
 t proved by Friedman and Tamari in the\nlate 1950s (but published in the l
 ate '60s).\n\nIn this talk\, I will describe a new\, constructive proof of
  the lattice\nproperty of the Tamari order\, which starts from the idea of
 \nreconsidering the order as a sequent calculus.  Along the way\, I will\n
 mention connections with the natural notion of "left representable"\nmulti
 category recently formulated by Bourke and Lack\, as well as some\nadditio
 nal motivations coming from the surprising combinatorics of\nlambda calcul
 us.\n\n(Based on the paper "A sequent calculus for a semi-associative law"
 \,\nto appear in LMCS. Link: https://arxiv.org/abs/1803.10080.)
LOCATION:MR4\, Centre for Mathematical Sciences
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