17,750 research outputs found
Promotion on oscillating and alternating tableaux and rotation of matchings and permutations
Using Henriques' and Kamnitzer's cactus groups, Sch\"utzenberger's promotion
and evacuation operators on standard Young tableaux can be generalised in a
very natural way to operators acting on highest weight words in tensor products
of crystals.
For the crystals corresponding to the vector representations of the
symplectic groups, we show that Sundaram's map to perfect matchings intertwines
promotion and rotation of the associated chord diagrams, and evacuation and
reversal. We also exhibit a map with similar features for the crystals
corresponding to the adjoint representations of the general linear groups.
We prove these results by applying van Leeuwen's generalisation of Fomin's
local rules for jeu de taquin, connected to the action of the cactus groups by
Lenart, and variants of Fomin's growth diagrams for the Robinson-Schensted
correspondence
Linear extensions and shelling orders
We prove that linear extensions of the Bruhat order of a matroid are shelling
orders and that the barycentric subdivision of a matroid is a Coxeter matroid,
viewing barycentric subdivisions as subsets of a parabolic quotient of a
symmetric group. A similar result holds for order ideals in minuscule quotients
of symmetric groups and in their barycentric subdivisions. Moreover, we apply
promotion and evacuation for labeled graphs of Malvenuto and Reutenauer to dual
graphs of simplicial complexes, providing promotion and evacuation of shelling
orders
Cyclic Sieving of Increasing Tableaux and small Schr\"oder Paths
An increasing tableau is a semistandard tableau with strictly increasing rows
and columns. It is well known that the Catalan numbers enumerate both
rectangular standard Young tableaux of two rows and also Dyck paths. We
generalize this to a bijection between rectangular 2-row increasing tableaux
and small Schr\"oder paths. We demonstrate relations between the jeu de taquin
for increasing tableaux developed by H. Thomas and A. Yong and the
combinatorics of tropical frieze patterns. We then use this jeu de taquin to
present new instances of the cyclic sieving phenomenon of V. Reiner, D.
Stanton, and D. White, generalizing results of D. White and of J. Stembridge.Comment: 20 page
Monodromy and K-theory of Schubert curves via generalized jeu de taquin
We establish a combinatorial connection between the real geometry and the
-theory of complex Schubert curves , which are
one-dimensional Schubert problems defined with respect to flags osculating the
rational normal curve. In a previous paper, the second author showed that the
real geometry of these curves is described by the orbits of a map on
skew tableaux, defined as the commutator of jeu de taquin rectification and
promotion. In particular, the real locus of the Schubert curve is naturally a
covering space of , with as the monodromy operator.
We provide a local algorithm for computing without rectifying the
skew tableau, and show that certain steps in our algorithm are in bijective
correspondence with Pechenik and Yong's genomic tableaux, which enumerate the
-theoretic Littlewood-Richardson coefficient associated to the Schubert
curve. We then give purely combinatorial proofs of several numerical results
involving the -theory and real geometry of .Comment: 33 pages, 12 figures including 2 color figures; to appear in the
Journal of Algebraic Combinatoric
FLA Tracking Chart 2008 Ashworth, Inc, India
The FLA uses Tracking Charts to provide the public with information about the compliance situation of individual factories - the specific problems that were found by monitors and the action taken by participating companies in response to the findings. These charts outline the series of events involved in the FLA independent external monitoring (IEM) process. These tracking charts report on the Ashworth factories in India where numerous violations were recorded by auditors in 2008
Tracking Chart 2004 Nike, South Korea 07004062C
This document is part of a digital collection provided by the Martin P. Catherwood Library, ILR School, Cornell University, pertaining to the effects of globalization on the workplace worldwide. Special emphasis is placed on labor rights, working conditions, labor market changes, and union organizing.FLA_2004_Nike_TC_South_Korea_07004062C.pdf: 15 downloads, before Oct. 1, 2020
Assessment Report 2013 River Cross, Mexico AA0000000324
This document is part of a digital collection provided by the Martin P. Catherwood Library, ILR School, Cornell University, pertaining to the effects of globalization on the workplace worldwide. Special emphasis is placed on labor rights, working conditions, labor market changes, and union organizing.FLA_2013_River_Cross_AR_Mexico_AA0000000324.pdf: 41 downloads, before Oct. 1, 2020
Some remarks on sign-balanced and maj-balanced posets
Let P be a poset with elements 1,2,...,n. We say that P is sign-balanced if
exactly half the linear extensions of P (regarded as permutations of 1,2,...,n)
are even permutations, i.e., have an even number of inversions. This concept
first arose in the work of Frank Ruskey, who was interested in the efficient
generation of all linear extensions of P. We survey a number of techniques for
showing that posets are sign-balanced, and more generally, computing their
"imbalance." There are close connections with domino tilings and, for certain
posets, a "domino generalization" of Schur functions due to Carre and Leclerc.
We also say that P is maj-balanced if exactly half the linear extensions of P
have even major index. We discuss some similarities and some differences
between sign-balanced and maj-balanced posets.Comment: 30 pages. Some inaccuracies in Section 3 have been corrected, and
Conjecture 3.6 has been adde
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