Abstract
A "dyadic rectangle" is a set of the form R = [a2-s, (a + 1)2-s] × [b2-t (b + 1)2-t], where s and t are nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study n-tilings, which consist of 2n nonoverlapping dyadic rectangles, each of area 2-n, whose union is the unit square. We discuss some of the underlying combinatorial structures, provide some efficient methods for uniformly sampling from the set of n-tilings, and study some limiting properties of random tilings.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 225-251 |
| Number of pages | 27 |
| Journal | Random Structures and Algorithms |
| Volume | 21 |
| Issue number | 3-4 |
| State | Published - Oct 2002 |
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ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Software
- Mathematics(all)
- Applied Mathematics
Cite this
Random Dyadic Tilings of the Unit Square. / Janson, Svante; Randall, Dana; Spencer, Joel.
In: Random Structures and Algorithms, Vol. 21, No. 3-4, 10.2002, p. 225-251.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Random Dyadic Tilings of the Unit Square
AU - Janson, Svante
AU - Randall, Dana
AU - Spencer, Joel
PY - 2002/10
Y1 - 2002/10
N2 - A "dyadic rectangle" is a set of the form R = [a2-s, (a + 1)2-s] × [b2-t (b + 1)2-t], where s and t are nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study n-tilings, which consist of 2n nonoverlapping dyadic rectangles, each of area 2-n, whose union is the unit square. We discuss some of the underlying combinatorial structures, provide some efficient methods for uniformly sampling from the set of n-tilings, and study some limiting properties of random tilings.
AB - A "dyadic rectangle" is a set of the form R = [a2-s, (a + 1)2-s] × [b2-t (b + 1)2-t], where s and t are nonnegative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study n-tilings, which consist of 2n nonoverlapping dyadic rectangles, each of area 2-n, whose union is the unit square. We discuss some of the underlying combinatorial structures, provide some efficient methods for uniformly sampling from the set of n-tilings, and study some limiting properties of random tilings.
UR - http://www.scopus.com/inward/record.url?scp=0036441047&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036441047&partnerID=8YFLogxK
M3 - Article
VL - 21
SP - 225
EP - 251
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
SN - 1042-9832
IS - 3-4
ER -