Olcay Coşkun

Tower tableaux

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only for reduced words which makes the algorithm a test for reducibility. Using the algorithm, a bijection between tower diagrams and finite permutations is obtained and it is shown that this bijection specializes to a bijection between certain labellings of a given tower diagram and reduced expressions of the corresponding permutation.

Inducing native Mackey functors to biset functors

In this paper, we describe the induction functor from the category of native Mackey functors to the category of biset functors for a finite group

Tower tableaux and Schubert polynomials

G

Tower diagrams and Pieri’s rule

over an algebraically closed field

The Dade group of Mackey functors for p-groups

k

Fibered p -biset Functor Structure of the Fibered Burnside Rings

of characteristic zero. We prove two applications of this description. As the first application, we exhibit that any projective biset functor over

Gluing Borel–Smith functions and the group of endo-trivial modules

k

Mackey functors, induction from restriction functors and coinduction from transfer functors

is induced from a (rational) virtual native Mackey functor. The second application is the explicit description of the projective indecomposable biset functors parameterized by simple groups.

Alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules

We prove that the well-known condition of being a balanced labeling can be characterized in terms of the sliding algorithm on tower diagrams. The characterization involves a generalization of authors@? Rothification algorithm. Using the characterization, we obtain descriptions of Schubert polynomials and Stanley symmetric functions.

A tate cohomology sequence for generalized Burnside rings

Abstract We introduce an algorithm to describe Pieri’s Rule for multiplication of Schubert polynomials. The algorithm uses tower diagrams introduced by the authors and another new algorithm that describes Monk’s Rule. Our result is different from the well-known descriptions (and proofs) of the rule by Bergeron–Billey and Kogan–Kumar and uses Sottile’s version of Pieri’s Rule.