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TORIC VARIETIES

- E. Elizondo, P. Lima-filho, F. Sottile, Z. Teitler
- 2010

We study toric varieties over a field k that split in a Galois extension K/k using Galois cohomology with coefficients in the toric automorphism group. This Galois cohomology fits into an exact… Expand

Combinatorial Hopf algebras and generalized Dehn–Sommerville relations

- M. Aguiar, N. Bergeron, F. Sottile
- MathematicsCompositio Mathematica
- 1 October 2003

A combinatorial Hopf algebra is a graded connected Hopf algebra over a field $\Bbbk$ equipped with a character (multiplicative linear functional) $\zeta\colon{\mathcal H}\to \Bbbk$. We show that the… Expand

Structure of The Malvenuto-Reutenauer Hopf Algebra of Permutations (Extended Abstract)

- M. Aguiar, F. Sottile
- Mathematics
- 11 March 2002

We analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive… Expand

Structure of the Loday–Ronco Hopf algebra of trees

- M. Aguiar, F. Sottile
- Mathematics
- 2 September 2004

Abstract Loday and Ronco defined an interesting Hopf algebra structure on the linear span of the set of planar binary trees. They showed that the inclusion of the Hopf algebra of non-commutative… Expand

Tableau Switching: Algorithms and Applications

- G. Benkart, F. Sottile, J. Stroomer
- Computer Science, MathematicsJ. Comb. Theory, Ser. A
- 1 October 1996

TLDR

Numerical Schubert Calculus

- Birkett Huber, F. Sottile, B. Sturmfels
- Mathematics, Computer ScienceJ. Symb. Comput.
- 10 June 1997

TLDR

Lower bounds for real solutions to sparse polynomial systems

- Evgenia Soprunova, F. Sottile
- Mathematics
- 27 September 2004

We show how to construct sparse polynomial systems that have non-trivial lower bounds on their numbers of real solutions. These are unmixed systems associated to certain polytopes. For the order… Expand

Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro

- F. Sottile
- Mathematics, Computer ScienceExp. Math.
- 24 April 1999

TLDR

Pieri's formula for flag manifolds and Schubert polynomials

- F. Sottile
- Mathematics
- 1996

© Annales de l’institut Fourier, 1996, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions… Expand

PIERI'S FORMULA VIA EXPLICIT RATIONAL EQUIVALENCE

- F. Sottile
- Mathematics
- 8 January 1996

Pieri's formula describes the intersection product of a Sc hubert cycle by a special Schubert cycle on a Grassmannian. We present a new geometric proof, exhibiting an explicit chain of rational… Expand

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