Macaulay2 » Documentation
Packages » Permutations :: exceedances
next | previous | forward | backward | up | index | toc

exceedances -- computes the exceedances of a permutation

Synopsis

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

Ways to use exceedances:

For the programmer

The object exceedances is a method function with options.