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# exceedances -- computes the exceedances of a permutation

- Usage:
    `exceedances w`
    `exceedances(w, Weak)`
- Inputs:
  - w, a permutation,
- Optional inputs:
  - Weak => ..., default value false
- Outputs:
  - a list,

## Description

A permutation $p=(p_1 \, \dots \, p_n)$ has an exceedance at $i$ if $p(i) > i$.

    i1 : p = permutation {3,1,2,5,4}

    o1 = Permutation{3, 1, 2, 5, 4}

    o1 : Permutation

    i2 : exceedances p

    o2 = {1, 4}

    o2 : List

This is called a weak exceedance if the inequality is not strict, i.e., $p(i) \geq i$.

    i3 : p = permutation {3,1,2,5,4}

    o3 = Permutation{3, 1, 2, 5, 4}

    o3 : Permutation

    i4 : exceedances(p, Weak=>true)

    o4 = {1, 4}

    o4 : List

## See also

- ascendingRuns -- computes the ascending runs of a permutation
- ascents -- computes the ascents of a permutation
- descendingRuns -- computes the descending runs of a permutation
- descents -- computes the descents of a permutation
- saliances -- computes the saliances of a permutation
- records -- computes the saliances of a permutation

## Ways to use exceedances:

- `exceedances(Permutation)`

## For the programmer

The object exceedances is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Permutations/Documentation/mainDocs.m2:224:0.