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2014 | 22 | 2 | 119-123
Tytuł artykułu

Bertrand’s Ballot Theorem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: A that receives n votes and B that receives k votes, and additionally n ≥ k. Then this theorem states that the probability of the situation where A maintains more votes than B throughout the counting of the ballots is equal to (n − k)/(n + k). This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.
Słowa kluczowe
Wydawca
Rocznik
Tom
22
Numer
2
Strony
119-123
Opis fizyczny
Daty
otrzymano
2014-06-13
online
2015-02-05
Twórcy
autor
  • Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland
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] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.
  • [5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990.
  • [6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.
  • [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.
  • [8] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661–668, 1990.
  • [9] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.
  • [10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.
  • [11] Artur Korniłowicz. On the real valued functions. Formalized Mathematics, 13(1):181–187, 2005.
  • [12] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887–890, 1990.
  • [13] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147–152, 1990.
  • [14] Karol Pąk. Cardinal numbers and finite sets. Formalized Mathematics, 13(3):399–406, 2005.
  • [15] Karol Pąk. The Catalan numbers. Part II. Formalized Mathematics, 14(4):153–159, 2006. doi:10.2478/v10037-006-0019-7.[Crossref]
  • [16] Jan Popiołek. Introduction to probability. Formalized Mathematics, 1(4):755–760, 1990.
  • [17] M. Renault. Four proofs of the ballot theorem. Mathematics Magazine, 80(5):345–352, December 2007.
  • [18] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115–122, 1990.
  • [19] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25–34, 1990.
  • [20] Andrzej Trybulec. On the decomposition of finite sequences. Formalized Mathematics, 5 (3):317–322, 1996.
  • [21] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329–334, 1990.
  • [22] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990.
  • [23] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.
  • [24] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825–829, 2001.
  • [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990.
  • [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_forma-2014-0014
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