Kassie Archer

Characterization of the allowed patterns of signed shifts

The allowed patterns of a map are those permutations in the same relative order as the initial segments of orbits realized by the map. In this paper, we characterize and provide enumerative bounds for the allowed patterns of signed shifts, a family of maps on infinite words.

Descents of λ -unimodal cycles in a character formula

We prove an identity conjectured by Adin and Roichman involving the descent set of λ -unimodal cyclic permutations. These permutations appear in formulas for characters of certain representations of the symmetric group. Such formulas have previously been proven algebraically. In this paper, we present a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.

Allowed patterns of symmetric tent maps via commuter functions

We introduce a new technique to study pattern avoidance in dynamical systems, namely the use of a commuter function between non-conjugate dynamical systems. We investigate the properties of such a commuter function, specifically

Cyclic permutations realized by signed shifts

h : [0,1] to [0,1]

Unimodal Permutations and Almost-Increasing Cycles

satisfying

Enumeration of cyclic permutations in vector grid classes

T_1 circ h = h circ T_mu

Rooted forests that avoid sets of permutations

, where

On the number of cycles in Av(312,4321) and Av(321,4123).

T_mu

Involutions and the Gelfand character

denotes a symmetric tent map of height

Pattern restricted quasi-Stirling permutations

mu