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Random covers of finite homogeneous lattices
We develop and extend some results for the scheme of independent random elements distributed on a finite lattice. In particular, we introduce the concept of the cover of a homogeneous lattice Ln of rank n and derive the exact equations and estimations for the number of covers with a given number o...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2006
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| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/4437 |
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| Summary: | We develop and extend some results for the scheme of independent random elements
distributed on a finite lattice. In particular, we introduce the concept of the cover of
a homogeneous lattice Ln of rank n and derive the exact equations and estimations
for the number of covers with a given number of blocks and for the total covers
number of the lattice Ln. A theorem about the asymptotic normality of the blocks
number in a random equiprobable cover of the lattice Ln is proved. The concept of
the cover index of the lattice Ln, that extend the notion of the cover index of a finite
set by its independent random subsets, is introduced. Applying the lattice moments
method, the limit distribution as n→∞ for the cover index of a subspace lattice of
the n-dimensional vector space over a finite field is determined. |
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