Лемма 4. n элементтен жасалған орын ауыстырулардың саны n!-ға тең болады.
Дәлелдеуі: n=1 орын ауыстырулар саны n!=1.
n=2→n!=2;
n=3→n!=6;
n-1 үшін лемма дұрыс деп есептеп, n үшін дәлелдейік.
орын ауыстыруындағы -ң орнына ретімен 1, 2, …, n қойып орын ауыстыруларды санайық:
бұлардың саны n –ге тең әрбір орын ауыстыруға кіретін n-1 элементтен тұратын орын ауыстырулардың саны (n-1)!- ға тең. Сонда n элементтен тұратын орын ауыстырулар саны n(n-1)!=n(n-1)! болады.
Анықтама. i, j екілігі α орын ауыстыруында инверсия құрайды деп аталады, егер i>j болса немесе i символы j символынан бұрын кездесетін болса; inv(α) арқылы α орын ауыстыруындағы инверсиялардың санын белгілейміз.
Анықтама. Oрын ауыстыруы жұп деп аталады, егер жұп болса, тақ деп аталады, егер тақ болса.
Мысал: (1, 2, 3)- инверсия құрамайды –жұп; inv=0;
(2, 1, 3)-2, 1- инверсия құрайды- тақ; inv=1;
(2, 3, 1)-3,1 және 2,1 инверсия құрайды –жұп; invһ2.
Анықтама. Орын ауыстырудағы 2 символдың орындарын алмастыратын амалды транспозиция деп атайды.
Лемма. Транспозиция орын ауыстырудың жұптығын өзгертеді.
1) Транспозиция орын ауыстырудағы қатар тұрған i. j символдарының орындарын алмастыратын болсын, онда
i символы мен j символы енбейтін инверсиялар толық сақталады.
Егер ![](data:image/png;base64,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) мен жұптығы әр түрлі.
Онда орын ауыстыруын орын ауыстыруынан қатар тұрған 2 символдық транспозициясы арқылы келесі түрде алуға болады:
k рет транспозиция қолданылады.
-1 рет
k рет.
Достарыңызбен бөлісу: |