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CATEGORIES:Lab Lunch
SUMMARY:A sequent calculus for a semi-associative law - No
am Zeilberger\, Birmingham Theory Group
DTSTART:20171108T120000Z
DTEND:20171108T010000Z
UID:TALK2980AT
URL:/talk/index/2980
DESCRIPTION:The classical Tamari order is the partial order on
fully-bracketed words obtained by assuming that m
ultiplication is only "semi-associative" (ab)c <=
a(bc). In the talk I will describe a simple proof-
theoretic characterization of the Tamari order as
a sequent calculus with a weakened version of Lamb
ek's left rule for the non-commutative product. Th
e main result is a "focusing" property (a strength
ening of cut-elimination) for this sequent calculu
s\, which yields the following coherence theorem:
every valid entailment in the Tamari order has exa
ctly one focused derivation. One novel combinatori
al application of this coherence theorem is a new
proof of the Tutte-Chapoton formula for the number
of intervals in the Tamari lattice. Depending on
the interests of the audience and if time permits\
, I may also discuss how some of these ideas relat
e to a natural notion of "left representable" mult
icategory\, considered independently in recent wor
k of Bourke and Lack on skew monoidal categories.
(Based on a paper presented at FSCD 2017.)
LOCATION:CS 217
CONTACT:Dr Steve Vickers
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