Vol. 12, No. 2, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 15, Issue 1
Volume 14, Issue 2 (to appear)
Volume 14, Issue 1
Volume 13, Issue 1
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2693-3004
ISSN (print): 2693-2997
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Bimonotone subdivisions of point configurations in the plane

Elina Robeva and Melinda Sun

Vol. 12 (2021), No. 2, 125–138
DOI: 10.2140/astat.2021.12.125

Bimonotone subdivisions in two dimensions are subdivisions all of whose sides are vertical or have nonnegative slope. They correspond to statistical estimates of probability distributions of strongly positively dependent random variables. The number of bimonotone subdivisions compared to the total number of subdivisions of a point configuration provides insight into how often the random variables are positively dependent. We give recursions as well as formulas for the numbers of bimonotone and total subdivisions of 2 × n grid configurations in the plane. Furthermore, we connect the former to the large Schröder numbers. We also show that the numbers of bimonotone and total subdivisions of a 2 × n grid are asymptotically equal. We then provide algorithms for counting bimonotone subdivisions for any m × n grid. Finally, we prove that all bimonotone triangulations of an m × n grid are connected by flips. This gives rise to an algorithm for counting the number of bimonotone (and total) triangulations of an m × n grid.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

bimonotone, subdivisions, triangulations, log-concave densities, log-supermodular densities, MTP${}_2$
Mathematical Subject Classification
Primary: 52C05
Received: 13 September 2020
Revised: 10 August 2021
Accepted: 28 August 2021
Published: 13 December 2021
Elina Robeva
Department of Mathematics
University of British Columbia
Vancouver, BC
Melinda Sun
Massachusetts Institute of Technology
Cambridge, MA
United States