
TL;DR
This paper extends the concept of SL(k)-friezes to include configurations with a ragged boundary, introducing new characterizations, properties, and construction methods for these generalized juggler's friezes.
Contribution
It generalizes SL(k)-friezes by incorporating ragged boundary rows, providing multiple equivalent definitions, and establishing connections to Grassmannians and matrix twists.
Findings
Established equivalences via determinants, recurrences, and duality.
Generalized periodicity and duality properties.
Developed a construction method using matrix twists.
Abstract
This note generalizes -friezes to configurations of numbers in which one of the boundary rows has been replaced by a ragged edge (described by a juggling function). We provide several equivalent definitions/characterizations of these juggler's friezes, in terms of determinants, linear recurrences, and a dual juggler's frieze. We generalize classic results, such as periodicity, duality, and a parametrization by part of a Grassmannian. We also provide a method of constructing such friezes from certain matrices using the twist of a matrix.
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
TopicsMatrix Theory and Algorithms · Advanced Combinatorial Mathematics · Mathematics and Applications
