# equidistribution

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• noun

## Words related to equidistribution

### a flat distribution having equal frequencies of occurrence

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References in periodicals archive ?
One consequence of MacMahon's Equidistribution Theorem is a pair of recursions for the distributions of the inversion number and the major index over [G.
Such proofs would imply MacMahon's Equidistribution Theorem and provide a bijection between inversion number and major index.
1 is equivalent to the equidistribution of these statistics.
1 shows that our main theorem is equivalent to the equidistribution of the inversion number and major index over [G.
Burstein, A combinatorial proof of joint equidistribution of some pairs of permutation statistics, talk at Permutation Patterns 2012.
Using bijections between bicolored matchings and weighted Dyck paths with bicolored rises, we in fact prove equidistribution of set-valued statistics and their generating functions.
The equidistribution of the pairs (Rlminl, Lrmaxp) and (Cyc, Lrmaxp) on Sr for the special case when the corresponding Dyck path D (r) is of the form [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] was shown by Foata and Han [3].
Han, New permutation coding and equidistribution of set valued statistics, Theoret.
q=t], which is a consequence of the equidistribution of inv and maj on every inverse descent class, proved by Foata and Schutzenberger [7].
The equidistribution of inv and maj was first proved on permutations of multisets by P.
The equidistribution of area and pdinv follows from the fact that each [[[a.
Their work also proved equidistribution by type, cited as Theorem 1.
We close this section with the statement of the uniform equidistribution result of Athanasiadis and Reiner.
The involutions that we introduce for non-crossing Dyck paths to prove the equidistribution of the generalized returns are also essential in the construction of our bijection between 2-triangulations and pairs of non-crossing Dyck paths.
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