skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Bukh, Boris"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, Advances in Combinatorics)
    For a finite point set P⊂R^d, denote by diam(P) the ratio of the largest to the smallest distances between pairs of points in P. Let c_{d,α}(n) be the largest integer c such that any n-point set P⊂R^d in general position, satisfying diam(P)<αn^{1/d}, contains an c-point convex independent subset. We determine the asymptotics of c_{d,α}(n) as n→∞ by showing the existence of positive constants β=β(d,α) and γ=γ(d) such that βn^{(d−1)/(d+1)}≤c_{d,α}(n)≤γn^{(d−1)/(d+1)} for α≥2. 
    more » « less
    Free, publicly-accessible full text available January 29, 2026
  2. ; (, The Electronic Journal of Combinatorics)
    Given finite sets $$X_1,\dotsc,X_m$$ in $$\mathbb{R}^d$$ (with $$d$$ fixed), we prove that there are respective subsets $$Y_1,\dotsc,Y_m$$ with $$\lvert Y_i\rvert \geq \frac{1}{poly(m)}\lvert X_i\rvert$$ such that, for $$y_1\in Y_1,\dotsc,y_m\in Y_m$$, the orientations of the\linebreak $(d+1)$-tuples from $$y_1,\dotsc,y_m$$ do not depend on the actual choices of points $$y_1,\dotsc,y_m$$. This generalizes previously known case when all the sets $$X_i$$ are equal. Furthermore, we give a construction showing that polynomial dependence on $$m$$ is unavoidable, as well as an algorithm that approximates the best-possible constants in this result. 
    more » « less
    Full Text Available 
  3. ; (, arxiv)
    Accepted Manuscript Full Text Available
  4. ; (, SIAM Journal on Discrete Mathematics)
    Full Text Available 
  5. ; (, Israel Journal of Mathematics)
    https://arxiv.org/abs/2203.12063 
    more » « less
    Accepted Manuscript Full Text Available
  6. ; ; (, IEEE Transactions on Information Theory)
    Full Text Available