556 research outputs found
An explicit derivation of the Mobius function for Bruhat order
We give an explicit nonrecursive complete matching for the Hasse diagram of
the strong Bruhat order of any interval in any Coxeter group. This yields a new
derivation of the Mobius function, recovering a classical result due to Verma.Comment: 9 pages; final versio
Teaching models and localāarea networks
The thesis of this paper is that new advances in both microtechnology and LAN technology can now provide teachers with flexible and exciting instructional tools which allow for a powerful integration of teaching model, curriculum content and technology. The first section describes some of the current applications of schoolābased LANs. The second section discusses various teaching models, and describes an inādepth example of how a teacher may go about providing instruction by combining a LAN and these models. The third section addresses the feasibility of such an instructional approach
Abacus models for parabolic quotients of affine Weyl groups
We introduce abacus diagrams that describe minimal length coset
representatives in affine Weyl groups of types B, C, and D. These abacus
diagrams use a realization of the affine Weyl group of type C due to Eriksson
to generalize a construction of James for the symmetric group. We also describe
several combinatorial models for these parabolic quotients that generalize
classical results in affine type A related to core partitions.Comment: 28 pages, To appear, Journal of Algebra. Version 2: Updated with
referee's comment
The enumeration of fully commutative affine permutations
We give a generating function for the fully commutative affine permutations
enumerated by rank and Coxeter length, extending formulas due to Stembridge and
Barcucci--Del Lungo--Pergola--Pinzani. For fixed rank, the length generating
functions have coefficients that are periodic with period dividing the rank. In
the course of proving these formulas, we obtain results that elucidate the
structure of the fully commutative affine permutations.Comment: 18 pages; final versio
Leading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements
We show that the leading coefficient of the Kazhdan--Lusztig polynomial
known as is always either 0 or 1 when is a Deodhar
element of a finite Weyl group. The Deodhar elements have previously been
characterized using pattern avoidance by Billey--Warrington (2001) and
Billey--Jones (2007). In type , these elements are precisely the 321-hexagon
avoiding permutations. Using Deodhar's (1990) algorithm, we provide some
combinatorial criteria to determine when for such permutations
.Comment: 28 page
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