# On a Two-Dimensional Search Problem

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 3, page 219-230
- ISSN: 1310-6600

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topKolev, 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 -

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