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CATEGORIES:Category Theory Seminar
SUMMARY:A new proof of the lattice property of the Tamari
order - Noam Zeilberger (University of Birmingham)
DTSTART;TZID=Europe/London:20190205T141500
DTEND;TZID=Europe/London:20190205T151500
UID:TALK117853AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/117853
DESCRIPTION:The so-called "Tamari order" is the partial orderi
ng on\nfully-bracketed words induced by a "semi-as
sociative" law (ab)c <=\na(bc). Among its many re
markable properties\, the order induces a\nlattice
structure on the bracketings of a given word (kno
wn as the\n"Tamari lattice"\, or the "rotation lat
tice of binary trees")\, a\nnon-obvious fact that
was first proved by Friedman and Tamari in the\nla
te 1950s (but published in the late '60s).\n\nIn t
his talk\, I will describe a new\, constructive pr
oof 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 wi
ll\nmention connections with the natural notion of
"left representable"\nmulticategory recently form
ulated by Bourke and Lack\, as well as some\naddit
ional motivations coming from the surprising combi
natorics of\nlambda calculus.\n\n(Based on the pap
er "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
CONTACT:Tamara von Glehn
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