exercise:03c9d37162: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Modify the program ''' AllPermutations''' to count the number of permutations of <math>n</math> objects that have exactly <math>j</math> fixed points for <math>j = 0</math>, 1, 2, \dots, <math>n</math>. Run your program for <math>n = 2</math> to...") |
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Modify the program ''' AllPermutations''' to count the number of permutations of <math>n</math> objects that have exactly <math>j</math> fixed points for <math>j = 0, 1, 2,...,n</math>. Run your program for <math>n = 2</math> to 6. Make a conjecture for the relation | |||
of permutations of <math>n</math> objects that have exactly <math>j</math> fixed points for <math>j = 0 | |||
between the number that have 0 fixed points and the number that have exactly 1 fixed | between the number that have 0 fixed points and the number that have exactly 1 fixed | ||
point. A proof of the correct conjecture can be found in Wilf.<ref group="Notes" >H. S. | point. A proof of the correct conjecture can be found in Wilf.<ref group="Notes" >H. S. | ||
Latest revision as of 22:52, 12 June 2024
Modify the program AllPermutations to count the number of permutations of [math]n[/math] objects that have exactly [math]j[/math] fixed points for [math]j = 0, 1, 2,...,n[/math]. Run your program for [math]n = 2[/math] to 6. Make a conjecture for the relation between the number that have 0 fixed points and the number that have exactly 1 fixed point. A proof of the correct conjecture can be found in Wilf.[Notes 1]
Notes