Shuffles on Coxeter groups
Swapneel Mahajan

TL;DR
This paper extends classical card shuffling methods to Coxeter groups of types B and D, introducing new shuffle models for signed decks and developing a shuffle algebra framework linked to Coxeter group geometry.
Contribution
It introduces new shuffles for Coxeter groups of types B and D and formalizes a shuffle algebra connecting algebraic and geometric structures.
Findings
Defined shuffles for signed decks corresponding to types B and D
Developed a shuffle algebra capturing algebraic and geometric relations
Discussed generalizations to buildings and q-analogues
Abstract
The random-to-top and the riffle shuffle are two well-studied methods for shuffling a deck of cards. These correspond to the symmetric group , i.e., the Coxeter group of type . In this paper, we give analogous shuffles for the Coxeter groups of type and . These can be interpreted as shuffles on a ``signed'' deck of cards. With these examples as motivation, we abstract the notion of a shuffle algebra which captures the connection between the algebraic structure of the shuffles and the geometry of the Coxeter groups. We also briefly discuss the generalisation to buildings which leads to q-analogues.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algorithms and Data Compression · Bayesian Methods and Mixture Models
