Several coin-tossing games are surveyed which, in a natural way, give rise to &#147;statistically&#148; induced probability measures on the set of permutations of <mml:math alttext="$\left\{ {1,2, \ldots ,n} \right\}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#8230;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math> and on sets of multipermutations. The distributions of a general class of random variables known as binary tree statistics are also given.

International Journal of Mathematics and Mathematical Sciences

Bernoulli trials and permutation statistics

Abstract

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