Geodesic
Coding parking functions by pairs of permutations
The electronic journal of combinatorics, Tome 10 (2003)

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Zbl EuDML
We introduce a new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length $n$ and the set of parking functions of length $n$. For all $u$ and $v=0,1,2,3$ and all $n\le 7$ we describe in terms of admissible pairs the dimensions of the bi-graded components $h_{u,v}$ of diagonal harmonics ${\Bbb{C}}[x_1,\dots,x_n;y_1,\dots,y_n]/S_n$, i.e., polynomials in two groups of $n$ variables modulo the diagonal action of symmetric group $S_n$.
DOI : 10.37236/1716
Classification : 05A15, 05A19, 16S36 
Yurii Burman; Michael Shapiro. Coding parking functions by pairs of permutations. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1716
@article{10_37236_1716,
     author = {Yurii Burman and Michael Shapiro},
     title = {Coding parking functions by pairs of permutations},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1716},
     zbl = {1023.05007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1716/}
}
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