P. Simecek, M. Studeny:
Vyuziti pojmu Hilbertovy baze pro overovani hypotezy o shodnosti strukturalnich a
kombinatorickych imsetu (in Czech, translation: The use of the concept of a Hilbert
basis to verify a hypothesis about the coincidence of structural and combinatorial
imsets), in ROBUST 2004 Sbornik praci trinacte letni skoly JCMF
(J. Antoch, G. Dohnal eds.), Trest, Czech Republic, JÈMF 2004, pp. 395-401.
This is a paper describing computer experiments made by student Petr Simecek,
whose aim was to confirm or disprove a conjecture (Question 7) from
- M. Studeny:
Probabilistic Conditional Independence Structures. Springer-Verlag, London, 2005.
The conjecture was confirmed in some special cases.
- Abstract
- Tento prispevek se venuje reseni klicoveho problemu z oblasti popisu struktur
podminene nezavislosti (mezi N nahodnymi velicinami) pomoci tzv. imsetu a
to overovani hypotezy o shodnosti mnozin strukturalnich a kombinatorickych imsetu.
- A
pdf version (178kB) is available.
The paper builds on the following publications:
- A. Schrijver: Theory of Linear and Integer Programming.
John Wiley, 1986.
- M. Studeny, R.R. Bouckaert, T. Kocka:
Extreme supermodular set functions over five variables.
Research report n. 1977,
Institute of Information Theory and Automation,
Prague, January 2000 (32 pages).
- M. Studeny:
Probabilistic Conditional Independence Structures. Springer-Verlag, London, 2005.