Flexary Operations

Karol Pąk

Formalized Mathematics (2015)

  • Volume: 23, Issue: 2, page 81-92
  • ISSN: 1426-2630

Abstract

top
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].

How to cite

top

Karol Pąk. "Flexary Operations." Formalized Mathematics 23.2 (2015): 81-92. <http://eudml.org/doc/271785>.

@article{KarolPąk2015,
abstract = {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].},
author = {Karol Pąk},
journal = {Formalized Mathematics},
keywords = {summation method; flexary plus; matrix generalization},
language = {eng},
number = {2},
pages = {81-92},
title = {Flexary Operations},
url = {http://eudml.org/doc/271785},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Karol Pąk
TI - Flexary Operations
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 2
SP - 81
EP - 92
AB - 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].
LA - eng
KW - summation method; flexary plus; matrix generalization
UR - http://eudml.org/doc/271785
ER -

References

top
  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. [2] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990. 
  3. [3] Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992. 
  4. [4] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  5. [5] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  6. [6] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  7. [7] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996. 
  8. [8] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  9. [9] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. 
  10. [10] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  11. [11] Czesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  12. [12] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  13. [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. Zbl1276.03030
  14. [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. Zbl1276.03032
  15. [15] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  16. [16] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001. 
  17. [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. [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. [19] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. 
  20. [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. [21] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
  22. [22] Konrad Raczkowski and Andrzej Nedzusiak. Real exponents and logarithms. Formalized Mathematics, 2(2):213-216, 1991. 
  23. [23] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990. 
  24. [24] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003. 
  25. [25] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  26. [26] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990. 
  27. [27] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1 (5):979-981, 1990. 
  28. [28] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  29. [29] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001. 
  30. [30] Freek Wiedijk. Formalizing 100 theorems. 
  31. [31] Herbert S. Wilf. Lectures on integer partitions. 
  32. [32] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990. 
  33. [33] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.