2 research outputs found
Enumeration of the distinct shuffles of permutations
A shuffle of two words is a word obtained by concatenating the two original words in either order and then sliding any letters from the second word back past letters of the first word, in such a way that the letters of each original word remain spelled out in their original relative order. Examples of shuffles of the words and are, for instance, and . In this paper, we enumerate the distinct shuffles of two permutations of any two lengths, where the permutations are written as words in the letters and , respectively
Bubble Lattices I: Structure
C. Greene introduced the shuffle lattice as an idealized model for DNA
mutation and discovered remarkable combinatorial and enumerative properties of
this structure. We attempt an explanation of these properties from a
lattice-theoretic point of view. To that end, we introduce and study an order
extension of the shuffle lattice, the bubble lattice. We characterize the
bubble lattice both locally (via certain transformations of shuffle words) and
globally (using a notion of inversion set). We then prove that the bubble
lattice is extremal and constructable by interval doublings. Lastly, we prove
that our bubble lattice is a generalization of the Hochschild lattice studied
earlier by Chapoton, Combe and the second author.Comment: 24 pages, 8 figures. Comments are welcom