We introduce the notion of a permanent [13] of a square matrix. It is a notion somewhat related to a determinant, so we follow closely the approach and theorems already introduced in the Mizar Mathematical Library for the determinant. Unfortunately, the formalization of the latter notion is at its early stage, so we had to prove many very elementary auxiliary facts.
@article{bwmeta1.element.doi-10_2478_v10037-006-0003-2,
author = {Ewa Romanowicz and Adam Grabowski},
title = {On the Permanent of a Matrix},
journal = {Formalized Mathematics},
volume = {14},
year = {2006},
pages = {13-20},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0003-2}
}
Ewa Romanowicz; Adam Grabowski. On the Permanent of a Matrix. Formalized Mathematics, Tome 14 (2006) pp. 13-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0003-2/
[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
[3] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
[4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
[5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
[6] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
[7] Czesław Byliński. Semigroup operations on finite subsets. Formalized Mathematics, 1(4):651-656, 1990.
[8] Czesław Byliński. Some properties of restrictions of finite sequences. Formalized Mathematics, 5(2):241-245, 1996.
[9] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
[10] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.
[11] Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.
[12] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
[13] H. Minc. Permanents. Addison-Wesley, 1978.
[14] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
[15] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
[16] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
[17] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
[19] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.
[20] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.
[21] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
[22] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
[23] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
[24] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991.
[25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
[26] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
[27] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.