Sets of Complex Unit Vectors with Two Angles and Distance-Regular Graphs
Junbo Huang

TL;DR
This paper explores special sets of complex unit vectors with two fixed angles, using distance-regular graphs to construct and analyze these sets, establishing bounds and characterizations for their sizes.
Contribution
It introduces new constructions of {0,α}-sets via distance-regular graphs and characterizes graphs that achieve size bounds.
Findings
Bounds for sizes of {0,α}-sets of flat vectors
Characterization of graphs meeting size bounds
New constructions of {0,α}-sets using distance-regular graphs
Abstract
We study {0,\alpha}-sets, which are sets of unit vectors of in which any two distinct vectors have angle 0 or \alpha. We investigate some distance-regular graphs that provide new constructions of {0,\alpha}-sets using a method by Godsil and Roy. We prove bounds for the sizes of {0,\alpha}-sets of flat vectors, and characterize all the distance-regular graphs that yield {0,\alpha}-sets meeting the bounds at equality.
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
TopicsMathematical Approximation and Integration · Finite Group Theory Research · graph theory and CDMA systems
