Random Sequences
(Sequence elements ordered)
by
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Consider a set of k elements. Let the elements be the first k positive integers. Consider the permutation set that corresponds to the first k positive integers - and let each element's order equal that element's value.
At every line of the permutation set, there exists an element or there exist the elements of the greatest order so far while doing a left - to - right scan. As a consequence, six permutation set properties exist. Expectations and Expected Values corresponding to the properties are calculated.
Then the order of the elements is generalized. An equal order constraint can be applied so that selected elements of adjacent order are reassigned the lowest order of the elements of adjacent order. Then multiple equal order constraints can be applied concurrently. Then all possible equal order constraints are considered.
Permutation sets are used to express random sequences. Equal order constraints are applied to the elements of the permutation sets. Values of permutation set properties are calculated and mathematical patterns are discerned. Consequently the interaction of order and random sequences is determined.
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About the Book
Consider a set of k elements. Let the elements be the first k positive integers. Consider the permutation set that corresponds to the first k positive integers – and let each element’s order equal that element’s value.
At every line of the permutation set, there exists an element or there exist the elements of the greatest order so far while doing a left-to-right scan. As a consequence, six permutation set properties exist. Expectations and expected values corresponding to the properties are calculated.
Then the order of the elements is generalized. An equal order constraint can be applied so that selected elements of adjacent order are reassigned the lowest order of the elements of adjacent order. Then multiple equal order constraints can be applied concurrently. Then all possible equal order constraints are considered.
Permutation sets are used to express random sequences. Equal order constraints are applied to the elements of the permutation sets. Values of permutation set properties are calculated and mathematical patterns are discerned. Consequently, the interaction of order and random sequences is determined.
About the Author
James Michael Foley is retired from a career as a mathematician for the federal government. He had the idea for this book when he was a graduate student at the University of Delaware. He earned his bachelor’s degree in mathematics from Towson University in 1964.