1,720,973 research outputs found
Stanley's work on unimodality
Get PDFThis paper surveys Stanley's work on unimodality, and its impact. It also poses some open problems that arise naturally from his work in this area
Some open problems on Coxeter groups and unimodality
No full textIn this paper I present some open problems on Coxeter groups
and unimodality, together with the main partial results, and computational
evidence, that are known about them
Linear Recurrences for Cylindrical Networks
No full textAbstract
We prove a general theorem that gives a linear recurrence for tuples of paths in every cylindrical network. This can be seen as a cylindrical analog of the Lindström–Gessel–Viennot theorem. We illustrate the result by applying it to Schur functions, plane partitions, and domino tilings.</jats:p
Affine geometric crystals in unipotent loop groups
No full textWe study products of the affine geometric crystal of type
A
A
corresponding to symmetric powers of the standard representation. The quotient of this product by the
R
R
-matrix action is constructed inside the unipotent loop group. This quotient crystal has a semi-infinite limit, where the crystal structure is described in terms of limit ratios previously appearing in the study of total positivity of loop groups.</p
under the direction of
No full textWe develop new methods for investigating problems of zero-sum type in general finite groups. We establish a new bound on Davenport’s constant for abelian groups that assymptotically improves the previously known bounds. We use tools from Representation Theory to study properties of zero-sum sequences through nilpotent ideals of group algebras. A new relation-ship between zero-sum problems and multidimensional covers of Z is also established.
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