Question

[tex] Sa~se~scrie~ca~produs~de~transpozitii~:\\\\ \[
a = \bigl(\begin{smallmatrix}
1 & 2 & 3 & 4 & 5 \\
5 & 4 & 2 & 3 & 1
\end{smallmatrix}\bigr)
\] [/tex]


Mie mi-a dat produsul (15)(24)(34). La sfarsit e altceva...

Answer 1

[tex]\text{Ti-am mai explicat odata cum se descompune o permutare in produs } \\ \text{de transpozitii. Cautam prima "abatere" si observam ca }\alpha (1)=5\neq 1,\\ \text{deci inmultim cu }(1,5).\\ (1,5)\cdot \alpha = 1\ 2\ 3\ 4\ 5\\ ~~~~~~~~~~~~~~~~ 1\ 4\ 2\ 3\ 5\\ \text{Urmatoarea abatere este }\alpha (2)=4\neq 2\\ (2,4)\cdot (1,5)\cdot \alpha= 1\ 2\ 3\ 4\ 5\\ ~~~~~~~~~~~~~~~~~~~~~~~~~ 1\ 2\ 4\ 3\ 5\\ \text{Observam ca }\\ (3,4)(2,4)(1,5)\alpha = e\\ \text{Deci }\alpha =(1,5)(2,4)(3,4)[/tex]$\text{Ti-a dat bine,la sfarsit e gresit.}$