Abstract
This paper studies lower and upper bounds for the number of vertices of the polytope of stochastic tensors (i.e. triply stochastic arrays of dimension n). By using known results on polytopes (i.e. the Upper and Lower Bound Theorems), we present some new lower and upper bounds. We show that the new upper bound is tighter than the one recently obtained by Chang et al. [Ann Funct Anal. 2016;7(3):386–393] and also sharper than the one in Linial and Luria’s [Discrete Comput Geom. 2014;51(1);161–170]. We demonstrate that the analog of the lower bound obtained in such a way, however, is no better than the existing ones.
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.
