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: "Malen, Greg"

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. ; ; (, The Electronic Journal of Combinatorics)
    What is the maximum number of holes enclosed by a $$d$$-dimensional polyomino built of $$n$$ tiles? Represent this number by $$f_d(n)$$. Recent results show that $$f_2(n)/n$$ converges to $1/2$. We prove that for all $$d \geq 2$$ we have $$f_d(n)/n \to (d-1)/d$$ as $$n$$ goes to infinity. We also construct polyominoes in $$d$$-dimensional tori with the maximal possible number of holes per tile. In our proofs, we use metaphors from error-correcting codes and dynamical systems. 
    more » « less
    Full Text Available 
  2. ; ; ; ; ; ; ; (, Journal of Applied and Computational Topology)
    Full Text Available