permutation

(noun)

An ordering of a finite set of distinct elements.

Related Terms

Examples of permutation in the following topics:

  • All permutations (i.e. brute force)

    • The automorphisms in a graph can be identified by the brute force method of examining every possible permutation of the graph.
    • For graphs of more than a few actors, the number of permutations that need to be compared becomes extremely large.
    • The results of Networks>Roles & Positions>Automorphic>All Permutations for this graph are shown in figure 14.2.
    • The algorithm examined over three hundred sixty two thousand possible permutations of the graph.
    • Automorphic equivalences by all permutations search for the Wasserman-Faust network

  • Permutations of Distinguishable Objects

    • The number of permutations of distinct elements can be calculated when not all elements from a given set are used.
    • $ possible permutations, where $n$ represents the number of objects.
    • It is easy enough to use this formula to count the number of possible permutations of a set of distinct objects; for example, the number of permutations of three differently-colored balls.
    • In this case, not all of the cards from the deck are chosen for each possible permutation.
    • Calculate the number of permutations of $n$ objects taken $k$ at a time

  • Permutations

    • A permutation of a set of objects is an arrangement of those objects in a particular order; the number of permutations can be counted.
    • One might define an anagram of a word as a permutation of its letters.
    • The number of permutations of $n$ distinct objects is given by:
    • In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values.
    • The study of permutations generally belongs to the field of combinatorics.

  • Permutations of Nondistinguishable Objects

    • Recall that the number of possible permutations of a set of $n$ distinct elements is given by $n!
    • When we encounter multiplicity in a permutation, we must account for it by dividing these possible arrangements out of the total number of permutations that would be possible if all of the elements were distinct.
    • Thus, the number of possible distinct permutations in the set is:
    • Thus, the number of possible distinct permutations can be calculated by:
    • Calculate the number of permutations of a given set of objects, some being nondistinguishable

  • Permutations and Combinations

    • More formally, this question is asking for the number of permutations of four things taken two at a time.
    • where nPr is the number of permutations of n things taken r at a time.
    • It is important to note that order counts in permutations.
    • Therefore permutations refer to the number of ways of choosing rather than the number of possible outcomes.
    • Unlike permutations, order does not count.

  • Theoretical Probability

    • Each sequence is called a permutation (or ordering) of the five items.
    • A permutation is an arrangement of unique objects in which order is important.
    • In other words, permutations using all the objects: $n$ objects, arranged into group size of $n$ without repetition, and order being important.
    • The number of possible permutations of a set size of $n$ in which $k$ elements are drawn can be calculated by:
    • By the Fundamental Rule of Counting, the total number of possible sequences of choices is a permutation of each of the items.

  • Categorical REGE for directed binary data (Wasserman-Faust directed data)

    • Once a regular equivalence blocking has been achieved, it is usually a good idea to produce a permuted and blocked version of the original data so that you can see the tie profiles of each of the classes.
    • One way to do this is to save the permutation vector from Network>Roles & Positions>Maximal Regular>CATREGE, and use it to permute the original data (Data>Permute).

  • Combinations

    • A combination is a way of selecting several things out of a larger group, where (unlike permutations) order does not matter.
    • To approach such a question, begin with the permutations: how many possible poker hands are there, if order does matter?
    • Recall the permutation formula: $\displaystyle{\frac{n!}
    • In this case, we can calculate the number of permutations as:
    • is itself a permutation question.

  • Matrix permutation, blocks, and images

    • Shifting rows and columns (if you want to rearrange the rows, you must rearrange the columns in the same way, or the matrix won't make sense for most operations) is called "permutation" of the matrix.
    • Let's rearrange (permute) this so that the two males and the two females are adjacent in the matrix.
    • Matrix permutation (Data>Permute) simply means to change the order of the rows and columns.
    • UCINET includes tools that make permuting and blocking matrices rather easy.
    • The "PreImage" data set contains the original scores, but permuted; the "Reduced image dataset" contains a new block matrix containing the block densities.

  • Study questions

    • What does it mean to "permute" a matrix, and to "block" it?
    • Try permuting your matrix, and blocking it.