On a Two-Dimensional Search Problem

Kolev, Emil, and Landgev, Ivan. "On a Two-Dimensional Search Problem." Serdica Mathematical Journal 21.3 (1995): 219-230. <http://eudml.org/doc/11668>.

@article{Kolev1995,
abstract = {In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist infinitely many loose squares.},
author = {Kolev, Emil, Landgev, Ivan},
journal = {Serdica Mathematical Journal},
keywords = {Two-Dimensional Search Problem; search problem; rectangles; square},
language = {eng},
number = {3},
pages = {219-230},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On a Two-Dimensional Search Problem},
url = {http://eudml.org/doc/11668},
volume = {21},
year = {1995},
}

TY - JOUR
AU - Kolev, Emil
AU - Landgev, Ivan
TI - On a Two-Dimensional Search Problem
JO - Serdica Mathematical Journal
PY - 1995
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 21
IS - 3
SP - 219
EP - 230
AB - In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist infinitely many loose squares.
LA - eng
KW - Two-Dimensional Search Problem; search problem; rectangles; square
UR - http://eudml.org/doc/11668
ER -