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Bertrand’s Ballot Theorem

   | Jun 30, 2014
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Formalized Mathematics
Special Issue: 25 years of the Mizar Mathematical Library

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

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

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

[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.Search in Google Scholar

[5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990.Search in Google Scholar

[6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.Search in Google Scholar

[7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990.Search in Google Scholar

[8] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661–668, 1990.Search in Google Scholar

[9] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.Search in Google Scholar

[10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.Search in Google Scholar

[11] Artur Korniłowicz. On the real valued functions. Formalized Mathematics, 13(1):181–187, 2005.Search in Google Scholar

[12] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887–890, 1990.Search in Google Scholar

[13] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147–152, 1990.Search in Google Scholar

[14] Karol Pąk. Cardinal numbers and finite sets. Formalized Mathematics, 13(3):399–406, 2005.Search in Google Scholar

[15] Karol Pąk. The Catalan numbers. Part II. Formalized Mathematics, 14(4):153–159, 2006. doi:10.2478/v10037-006-0019-7.10.2478/v10037-006-0019-7Search in Google Scholar

[16] Jan Popiołek. Introduction to probability. Formalized Mathematics, 1(4):755–760, 1990.Search in Google Scholar

[17] M. Renault. Four proofs of the ballot theorem. Mathematics Magazine, 80(5):345–352, December 2007.10.1080/0025570X.2007.11953509Search in Google Scholar

[18] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115–122, 1990.Search in Google Scholar

[19] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25–34, 1990.Search in Google Scholar

[20] Andrzej Trybulec. On the decomposition of finite sequences. Formalized Mathematics, 5 (3):317–322, 1996.Search in Google Scholar

[21] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329–334, 1990.Search in Google Scholar

[22] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990.Search in Google Scholar

[23] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.Search in Google Scholar

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

[25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990.Search in Google Scholar

[26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990.Search in Google Scholar

eISSN:
1898-9934
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Computer Sciences, other, Mathematics, General Mathematics