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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
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Volume 18, Issue 4 (Jan 2010)

Issues

Counting Derangements, Non Bijective Functions and the Birthday Problem

Cezary Kaliszyk
  • Institut für Informatik I4, Techische Universität München, Boltzmannstraße 3 85748 Garching, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2011-01-05 | DOI: https://doi.org/10.2478/v10037-010-0023-9

Counting Derangements, Non Bijective Functions and the Birthday Problem

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].

  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Google Scholar

  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Google Scholar

  • [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • [4] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.Google Scholar

  • [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

  • [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [7] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Google Scholar

  • [8] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Google Scholar

  • [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.CrossrefGoogle Scholar

  • [10] Karol Pąk. Cardinal numbers and finite sets. Formalized Mathematics, 13(3):399-406, 2005.Google Scholar

  • [11] Konrad Raczkowski and Andrzej Nędzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.Google Scholar

  • [12] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Google Scholar

  • [13] Piotr Rudnicki and Andrzej Trybulec. Abian's fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.Google Scholar

  • [14] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.Google Scholar

  • [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [16] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.Google Scholar

  • [17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Google Scholar

  • [18] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.Google Scholar

About the article


Published Online: 2011-01-05

Published in Print: 2010-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0023-9.

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