Lattices on shuffle words

Algebra Seminar
Monday, November 28, 2022 - 1:30pm for 1 hour (actually 50 minutes)
Clough 125 Classroom
Thomas McConville – Kennesaw State University – tmcconvi@kennesaw.edu
Papri Dey

The shuffle lattice is a partial order on words determined by two common types of genetic mutation: insertion and deletion. Curtis Greene discovered many remarkable enumerative properties of this lattice that are inexplicably connected to Jacobi polynomials. In this talk, I will introduce an alternate poset called the bubble lattice. This poset is obtained from the shuffle lattice by including transpositions. Using the structural relationship between bubbling and shuffling, we provide insight into Greene’s enumerative results. This talk is based on joint work with Henri Mülle.