Geodesic
Monomial nonnegativity and the Bruhat order
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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We show that five nonnegativity properties of polynomials coincide when restricted to polynomials of the form $x_{1,\pi(1)}\cdots x_{n,\pi(n)} - x_{1,\sigma(1)}\cdots x_{n,\sigma(n)}$, where $\pi$ and $\sigma$ are permutations in $S_n$. In particular, we show that each of these properties may be used to characterize the Bruhat order on $S_n$.
DOI : 10.37236/1875
Classification : 05E05, 05A15, 06A07
Mots-clés : symmetric group, permutation matrix, Bruhat poset, Schur polynomials 
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     author = {Brian Drake and Sean Gerrish and Mark Skandera},
     title = {Monomial nonnegativity and the {Bruhat} order},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1875},
     zbl = {1076.05084},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1875/}
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Brian Drake; Sean Gerrish; Mark Skandera. Monomial nonnegativity and the Bruhat order. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1875

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