Henry Cohn and Abhinav Kumar
نویسندگان
چکیده
We use techniques of Bannai and Sloane to give a new proof that there is a unique (22, 891, 1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23, 4600, 1/3) spherical code.
منابع مشابه
Uniqueness of the ( 22 , 891 , 1 / 4 ) spherical code Henry Cohn and
We use techniques of Bannai and Sloane to give a new proof that there is a unique (22, 891, 1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23, 4600, 1/3) spherical code.
متن کاملA Conceptual Breakthrough in Sphere Packing
Henry Cohn is principal researcher at Microsoft Research New England and adjunct professor of mathematics at the Massachusetts Institute of Technology. His e-mail address is cohn@ microsoft.com. For permission to reprint this article, please contact: [email protected]. DOI: http://dx.doi.org/10.1090/noti1474 On March 14, 2016, the world of mathematics received an extraordinary Pi Day s...
متن کاملRigidity of spherical codes
A packing of spherical caps on the surface of a sphere (that is, a spherical code) is called rigid or jammed if it is isolated within the space of packings. In other words, aside from applying a global isometry, the packing cannot be deformed. In this paper, we systematically study the rigidity of spherical codes, particularly kissing configurations. One surprise is that the kissing configurati...
متن کاملGround states and formal duality relations in the Gaussian core model.
We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian ...
متن کاملAlgorithmic design of self-assembling structures.
We study inverse statistical mechanics: how can one design a potential function so as to produce a specified ground state? In this article, we show that unexpectedly simple potential functions suffice for certain symmetrical configurations, and we apply techniques from coding and information theory to provide mathematical proof that the ground state has been achieved. These potential functions ...
متن کامل