@MISC{MATRIX_9.MIZ,
  AUTHOR = {Romanowicz, Ewa and Grabowski, Adam},
  TITLE = {On the Permanent of a Matrix},
  SECTION1 = {Preliminaries},
  SECTION2 = {Permutations},
  SECTION3 = {The Permanent of a Matrix},
  SECTION4 = {Matrices with the Dimension 2 and 3},
  SECTION5 = {Transpositions},
  SECTION6 = {Even and Odd Permutations},
  SECTION7 = {Determinant and Permanent},
  SECTION8 = {On the Paths of Matrices},
  SECTION9 = {Auxiliary Lemmas for Further Work},
  DAY = {04},
  MONTH = {January},
  YEAR = {2006},
  ADDRESS1 = {Institute of Mathematics\\University of Bia{\l}ystok\\Akademicka 2, 15-267 Bia{\l}ystok, Poland},
  ADDRESS2 = {Institute of Mathematics\\University of Bia{\l}ystok\\Akademicka 2, 15-267 Bia{\l}ystok, Poland},
  SUMMARY = {We introduce the notion of a permanent \cite{Minc78}
  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.}}

