Abstract
Recent work by M. L. Eaton and the present authors reviews and generalizes work on majorization and group majorization. The standard material on majorization was extended from the symmetric group to more general groups in the important paper of Eaton and Perlman (1977). The present paper studies one special nonreflection group, namely the cyclic group on n elements. We say that a vector x cyclically majorizes a vector y, written y < C x, if it lies in the convex hull of all vectors which can be obtained from x by cyclic permutation. The class of order-preserving functions is studied, and the theory gives an ordering on the smoothness of periodic functions with possible application to time series analysis and also an ordering of smoothing operators.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
