ON THE NUMBER OF INVERSION OUTCOMES OF THE PERMUTATION SCHEME AND ITS ANALYSIS WITH FIXED NUMBER OF INVERSIONS

• Main Author: Natalia Enatskaya
• Format: Article
• Language: English
• Published: Karelian Research Centre of the Russian Academy of Sciences 2015-10-01
• Series: Transactions of the Karelian Research Centre of the Russian Academy of Sciences
• Subjects: enumeration of outcomes; permutation scheme; recurrence; number of inversions; modelling
• Online Access: http://journals.krc.karelia.ru/index.php/mathem/article/view/246

<pre>The numerical method of calculation of inversions in permutations uses the</pre><pre>method of graph theory. As the result we <span>colculate</span> the recurrence for <span>colculation</span> of the numbers of inversions with the use of the bunchs of graphs and finding the probability distribution of the number of inversions with the increes of the size of the permutanion.</pre><pre> </pre><pre>The scheme <span>definded</span> in its name is investigated by <span>asiding</span> some outcomes of the similar scheme without restriction. The number of outcomes of the scheme is obtained, the direct enumeration is fulfiled, thier probability distribution is finded the problem of their numeration is solved and the scheme suggested.</pre>