This article describes a new type of combinatorial numbers which calculate amount of the covers of a finite set by subsets having fixed cardinalities - parameters of numbers. A series of relations and identities are proved for them. Some sums of these numbers are computed. Special cases of new combinatorial numbers with parameters satisfying certain relations are investigated. Several other applications of these numbers in discrete mathematics are shown.
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- Title THE NUMBER OF DISORDERED COVERS OF A FINITE SET BY SUBSETS HAVING FIXED CARDINALITIES
- Headline THE NUMBER OF DISORDERED COVERS OF A FINITE SET BY SUBSETS HAVING FIXED CARDINALITIES
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 4(10)
- Date:
- DOI
Keywords
finite set, combinatoric numbers, cover, комбинаторные числа, конечное множество, покрытиеAuthors
References
Burger A. P., van Vuuren J. H. Balanced minimum covers of a finite set // Discrete Mathematics. 2007. V.307. No. 22. P. 2853-2860.
Айгнер М. Комбинаторная теория. М.: Мир, 1982.
Риордан Д. Введение в комбинаторный анализ. М.: ИЛ, 1963.
Холл М. Комбинаторика. М.: Мир, 1970.
Stanley R. P. Enumerative Combinatorics. V. I. Cambridge University Press, 2002.
<http://oeis.org/classic/A006129> - On-Line Encyclopedia of Integer Sequences - энциклопедии целочисленных последовательностей.
Эндрюс Г. Теория разбиений. М.: Наука, 1982.
Comtet L. Advanced Combinatorics. The Art of Finite and Infinate Expansions. Dordrecht, Holland: D. Reidel Publishing Company, 1974.
Macula A. J. Covers of a finite set // Mathematics Magazine. 1994. V. 67. No. 2. P. 141-144.
Кнут Д., Грэхем Ф., Поташник О. Конкретная математика. Основание информатики. М.: Мир, 2006.
THE NUMBER OF DISORDERED COVERS OF A FINITE SET BY SUBSETS HAVING FIXED CARDINALITIES | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2010. № 4(10).
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