Geodesic
The size of Fulton's essential set
The electronic journal of combinatorics, Tome 2 (1995)
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The essential set of a permutation was defined by Fulton as the set of southeast corners of the diagram of the permutation. In this paper we determine explicit formulas for the average size of the essential set in the two cases of arbitrary permutations in $S_n$ and $321$-avoiding permutations in $S_n$. Vexillary permutations are discussed too. We also prove that the generalized Catalan numbers ${r+k-1\choose n}-{r+k-1\choose n-2}$ count $r\times k$-matrices dotted with $n$ dots that are extendable to $321$-avoiding permutation matrices.
DOI : 10.37236/1200
Classification : 05A15, 05E99, 14M15
Mots-clés : Fulton's essential set, essential set of a permutation, Catalan numbers, matrices 
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     author = {Kimmo Eriksson and Svante Linusson},
     title = {The size of {Fulton's} essential set},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1200},
     zbl = {0814.05006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1200/}
}
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Kimmo Eriksson; Svante Linusson. The size of Fulton's essential set. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1200

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