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2010 | 18 | 4 | 197-200
Tytuł artykułu

Counting Derangements, Non Bijective Functions and the Birthday Problem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The article provides counting derangements of finite sets and counting non bijective functions. We provide a recursive formula for the number of derangements of a finite set, together with an explicit formula involving the number e. We count the number of non-one-to-one functions between to finite sets and perform a computation to give explicitely a formalization of the birthday problem. The article is an extension of [10].
Słowa kluczowe
Wydawca
Rocznik
Tom
18
Numer
4
Strony
197-200
Opis fizyczny
Daty
wydano
2010-01-01
online
2011-01-05
Twórcy
  • Institut für Informatik I4, Techische Universität München, Boltzmannstraße 3 85748 Garching, Germany
Bibliografia
  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [4] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [7] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [8] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  • [9] Yatsuka Nakamura and Hisashi Ito. Basic properties and concept of selected subsequence of zero based finite sequences. Formalized Mathematics, 16(3):283-288, 2008, doi:10.2478/v10037-008-0034-y.[Crossref]
  • [10] Karol Pąk. Cardinal numbers and finite sets. Formalized Mathematics, 13(3):399-406, 2005.
  • [11] Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.
  • [12] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  • [13] Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
  • [14] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [16] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
  • [17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [18] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-010-0023-9
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