45 research outputs found
On a Subposet of the Tamari Lattice
We explore some of the properties of a subposet of the Tamari lattice
introduced by Pallo, which we call the comb poset. We show that three binary
functions that are not well-behaved in the Tamari lattice are remarkably
well-behaved within an interval of the comb poset: rotation distance, meets and
joins, and the common parse words function for a pair of trees. We relate this
poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page
Tamari Lattices and the symmetric Thompson monoid
We investigate the connection between Tamari lattices and the Thompson group
F, summarized in the fact that F is a group of fractions for a certain monoid
F+sym whose Cayley graph includes all Tamari lattices. Under this
correspondence, the Tamari lattice operations are the counterparts of the least
common multiple and greatest common divisor operations in F+sym. As an
application, we show that, for every n, there exists a length l chain in the
nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page
Enfermedades y plagas que afectan la calidad de la semilla de papa y efecto de la seleccion positiva.
Short Communications: Calling all authors: Writing skills for family medicine residents in Kenya
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