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2015 | 23 | 2 | 93-99

Tytuł artykułu

Euler’s Partition Theorem

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Języki publikacji

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Abstrakty

EN
In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1]). Euler’s Partition Theorem is listed as item #45 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/ [27].

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Wydawca

Rocznik

Tom

23

Numer

2

Strony

93-99

Opis fizyczny

Daty

wydano
2015-06-01
otrzymano
2015-03-26
online
2015-08-13

Twórcy

autor
  • Institute of Informatics University of Białystok Ciołkowskiego 1M, 15-245 Białystok Poland

Bibliografia

  • [1] George E. Andrews and Kimmo Eriksson. Integer Partitions. ISBN 9780521600903.
  • [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [3] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
  • [4] Grzegorz Bancerek. Countable sets and Hessenberg’s theorem. Formalized Mathematics, 2(1):65-69, 1991.
  • [5] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [6] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [7] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [8] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  • [9] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [10] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [11] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [12] Czesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
  • [13] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [14] Marco B. Caminati. Preliminaries to classical first order model theory. Formalized Mathematics, 19(3):155-167, 2011. doi:10.2478/v10037-011-0025-2.
  • [15] Marco B. Caminati. First order languages: Further syntax and semantics. Formalized Mathematics, 19(3):179-192, 2011. doi:10.2478/v10037-011-0027-0.
  • [16] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [17] Magdalena Jastrzȩbska and Adam Grabowski. Some properties of Fibonacci numbers. Formalized Mathematics, 12(3):307-313, 2004.
  • [18] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  • [19] Karol Pak. Flexary operations. Formalized Mathematics, 23(2):81-92, 2015. doi:10.1515 /forma-2015-0008.
  • [20] Karol Pak. The Nagata-Smirnov theorem. Part II. Formalized Mathematics, 12(3):385-389, 2004.
  • [21] Karol Pak. Stirling numbers of the second kind. Formalized Mathematics, 13(2):337-345, 2005.
  • [22] Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997.
  • [23] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
  • [24] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [25] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.
  • [26] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [27] Freek Wiedijk. Formalizing 100 theorems.
  • [28] Herbert S. Wilf. Lectures on integer partitions.
  • [29] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [30] Bo Zhang and Yatsuka Nakamura. The definition of finite sequences and matrices of probability, and addition of matrices of real elements. Formalized Mathematics, 14(3): 101-108, 2006. doi:10.2478/v10037-006-0012-1.

Typ dokumentu

Bibliografia

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bwmeta1.element.doi-10_1515_forma-2015-0009
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