Sortability of Permutations in the Presence of an Adversary
Additional Funding Sources
This research, conducted at the Complexity Across Disciplines Research Experience for Undergraduates site, was supported by the National Science Foundation under Grant No. DMS-1659872 and by Boise State University.
Abstract
Ciliates are single-cell organisms with two nuclei. The DNA sorting processes that naturally occur in ciliates are analogous to two particular operations on permutations. These sorting operations are of combinatorial interest outside of biology. The operations are efficient but cannot sort everything. We look at the sortability of permutations through the lens of graph theory and matrices. If a permutations is sortable, we show that any possible sequence of these operations will sort it and give an efficient algorithm for determining sortability. In the unsortable case, this algorithm gives the possible termination states that can result from these sorting operations. In the cases where sorting doesn't work, we can represent the interactions between permutations from a game theoretic point of view. We examine one- and two-player games based on these permutations, and develop techniques for determining a winning strategy.
Sortability of Permutations in the Presence of an Adversary
Ciliates are single-cell organisms with two nuclei. The DNA sorting processes that naturally occur in ciliates are analogous to two particular operations on permutations. These sorting operations are of combinatorial interest outside of biology. The operations are efficient but cannot sort everything. We look at the sortability of permutations through the lens of graph theory and matrices. If a permutations is sortable, we show that any possible sequence of these operations will sort it and give an efficient algorithm for determining sortability. In the unsortable case, this algorithm gives the possible termination states that can result from these sorting operations. In the cases where sorting doesn't work, we can represent the interactions between permutations from a game theoretic point of view. We examine one- and two-player games based on these permutations, and develop techniques for determining a winning strategy.
Comments
W16