302 research outputs found
Symmetric Decompositions and the Strong Sperner Property for Noncrossing Partition Lattices
We prove that the noncrossing partition lattices associated with the complex
reflection groups for admit symmetric decompositions
into Boolean subposets. As a result, these lattices have the strong Sperner
property and their rank-generating polynomials are symmetric, unimodal, and
-nonnegative. We use computer computations to complete the proof that
every noncrossing partition lattice associated with a well-generated complex
reflection group is strongly Sperner, thus answering affirmatively a question
raised by D. Armstrong.Comment: 30 pages, 5 figures, 1 table. Final version. The results of the
initial version were extended to symmetric Boolean decompositions of
noncrossing partition lattice
Richard Stanley through a crystal lens and from a random angle
We review Stanley's seminal work on the number of reduced words of the
longest element of the symmetric group and his Stanley symmetric functions. We
shed new light on this by giving a crystal theoretic interpretation in terms of
decreasing factorizations of permutations. Whereas crystal operators on
tableaux are coplactic operators, the crystal operators on decreasing
factorization intertwine with the Edelman-Greene insertion. We also view this
from a random perspective and study a Markov chain on reduced words of the
longest element in a finite Coxeter group, in particular the symmetric group,
and mention a generalization to a poset setting.Comment: 11 pages; 3 figures; v2 updated references and added discussion on
Coxeter-Knuth grap
Braids, posets and orthoschemes
In this article we study the curvature properties of the order complex of a
graded poset under a metric that we call the ``orthoscheme metric''. In
addition to other results, we characterize which rank 4 posets have CAT(0)
orthoscheme complexes and by applying this theorem to standard posets and
complexes associated with four-generator Artin groups, we are able to show that
the 5-string braid group is the fundamental group of a compact nonpositively
curved space.Comment: 33 pages, 16 figure
Decomposition and enumeration in partially ordered sets
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.Includes bibliographical references (p. 123-126).by Patricia Hersh.Ph.D
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