Matching fixed rectangles in 2-dimension

Ke-Ning Sheng and Joseph I. Naus

Statistics & Probability Letters, 1996, vol. 26, issue 1, 83-90

Abstract: For each element Xi,j(1 [less-than-or-equals, slant] i [less-than-or-equals, slant] M, 1 [less-than-or-equals, slant] j [less-than-or-equals, slant] T) in an M by T 2-dimensional random rectangular lattice, let the Xi,j's be independently, identically distributed and P{Xi,j = 1} = p [epsilon] (0, 1), P{Xi,j [not equal to] 1} = 1 - p. We find the probability, ifP{n, k vb M, T}, that there exists a smaller fixed (n by k) rectangle of all 1's in the M by T random rectangular lattice. Exact results for the special cases M = n,n + 1,n + 2 and approximations and upper bounds of the probability in the general case are given and evaluated.

Keywords: Probability; Largest; rectangle; Matching; Lattice (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (1)

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