# Counting Derangements, Non Bijective Functions and the Birthday Problem

Formalized Mathematics (2010)

- Volume: 18, Issue: 4, page 197-200
- ISSN: 1426-2630

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topCezary Kaliszyk. "Counting Derangements, Non Bijective Functions and the Birthday Problem." Formalized Mathematics 18.4 (2010): 197-200. <http://eudml.org/doc/266571>.

@article{CezaryKaliszyk2010,

abstract = {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].},

author = {Cezary Kaliszyk},

journal = {Formalized Mathematics},

language = {eng},

number = {4},

pages = {197-200},

title = {Counting Derangements, Non Bijective Functions and the Birthday Problem},

url = {http://eudml.org/doc/266571},

volume = {18},

year = {2010},

}

TY - JOUR

AU - Cezary Kaliszyk

TI - Counting Derangements, Non Bijective Functions and the Birthday Problem

JO - Formalized Mathematics

PY - 2010

VL - 18

IS - 4

SP - 197

EP - 200

AB - 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].

LA - eng

UR - http://eudml.org/doc/266571

ER -

## References

top- [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. Zbl06213858
- [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.

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