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 cove...
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| Date: | 2006 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/4437 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Random covers of finite homogeneous lattices / A.N. Alekseychuk // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 12–19. — Бібліогр.: 10 назв.— англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862580515495739392 |
|---|---|
| author | Alekseychuk, A.N. |
| author_facet | Alekseychuk, A.N. |
| citation_txt | Random covers of finite homogeneous lattices / A.N. Alekseychuk // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 12–19. — Бібліогр.: 10 назв.— англ. |
| collection | DSpace DC |
| description | 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.
|
| first_indexed | 2025-11-26T20:52:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-4437 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0321-3900 |
| language | English |
| last_indexed | 2025-11-26T20:52:07Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Alekseychuk, A.N. 2009-11-10T14:48:05Z 2009-11-10T14:48:05Z 2006 Random covers of finite homogeneous lattices / A.N. Alekseychuk // Theory of Stochastic Processes. — 2006. — Т. 12 (28), № 1-2. — С. 12–19. — Бібліогр.: 10 назв.— англ. 0321-3900 https://nasplib.isofts.kiev.ua/handle/123456789/4437 519.21 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. en Інститут математики НАН України Random covers of finite homogeneous lattices Article published earlier |
| spellingShingle | Random covers of finite homogeneous lattices Alekseychuk, A.N. |
| title | Random covers of finite homogeneous lattices |
| title_full | Random covers of finite homogeneous lattices |
| title_fullStr | Random covers of finite homogeneous lattices |
| title_full_unstemmed | Random covers of finite homogeneous lattices |
| title_short | Random covers of finite homogeneous lattices |
| title_sort | random covers of finite homogeneous lattices |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/4437 |
| work_keys_str_mv | AT alekseychukan randomcoversoffinitehomogeneouslattices |