Flexary Operations

• Autorzy: Karol Pąk
• Języki publikacji: EN

Abstrakty

EN

In this article we introduce necessary notation and definitions to prove the Euler’s Partition Theorem according to H.S. Wilf’s lecture notes [31]. Our aim is to create an environment which allows to formalize the theorem in a way that is as similar as possible to the original informal proof. 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/ [30].

Słowa kluczowe

EN

summation method; flexary plus; matrix generalization

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 2
• Strony: 81-92

Daty

wydano

2015-06-01

otrzymano

2015-03-26

online

2015-08-13

Twórcy

autor

Karol Pąk

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

Bibliografia

• [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [2] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990.
• [3] Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992.
• [4] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• [5] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
• [6] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [7] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.
• [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. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
• [12] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [13] Marco B. Caminati. Preliminaries to classical first order model theory. Formalized Mathematics, 19(3):155-167, 2011. doi:10.2478/v10037-011-0025-2.
• [14] Marco B. Caminati. First order languages: Further syntax and semantics. Formalized Mathematics, 19(3):179-192, 2011. doi:10.2478/v10037-011-0027-0.
• [15] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
• [16] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.
• [17] Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin’s test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317-321, 1998.
• [18] Artur Korniłowicz. Arithmetic operations on functions from sets into functional sets. Formalized Mathematics, 17(1):43-60, 2009. doi:10.2478/v10037-009-0005-y.
• [19] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
• [20] 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.
• [21] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
• [22] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991.
• [23] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
• [24] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
• [25] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
• [26] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.
• [27] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1 (5):979-981, 1990.
• [28] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [29] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.
• [30] Freek Wiedijk. Formalizing 100 theorems.
• [31] Herbert S. Wilf. Lectures on integer partitions.
• [32] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
• [33] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

Identyfikatory

DOI

10.1515/forma-2015-0008