Frank Sottile: Papers in Combinatorics

Papers in Geometry,   Schubert calculus,   Combinatorial Hopf Algebras,   Real Algebraic Geometry,   Computational Algebraic Geometry,   Applicable Algebraic Geometry,   and   Computational Geometry.

1	A Littlewood-Richardson rule for Grassmannian permutations with Kevin Purbhoo. Proc. Amer. Math. Soc., to appear. ArXiv.org/0708.1582. 9 pages.
2	The recursive nature of cominuscule Schubert calculus with Kevin Purbhoo Advances in Mathematics, 217 (2008), pp. 1962--2004.
3	The equivariant cohomology rings of quot schemes, with Tom Braden, and Linda Chen. Pacific Journal of Mathematics, 238, No. 2 (2008) 201--232.
4	(Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones), with Matthias Beck and Christian Haase. Mathematical Intelligencer, to appear. 15 pages. math.CO/0506466.
5	Irrational proofs of three theorems of Stanley, with Matthias Beck, European Journal of Combinatorics, 28, Issue 1, January 2007, 403-409.
6	A Pieri-type formula for the K-theory of a flag manifold, with Cristian Lenart, Trans. Amer. Math. Soc., Trans. Amer. Math. Soc. 359 (2007), 2317--2342.
7	Grothendieck Polynomials via Permutation Patterns and chains in the Bruhat Order, with Cristian Lenart and Shawn Robinson. American Journal of Mathematics, 128, No. 4, (2006), 805--848.
8	Lower Bounds for Real Solutions to Sparse Polynomial Systems, with Evgenia Soprunova, Advances in Mathematics, Volume 204, Issue 1, 1 August 2006, Pages 116-151.
9	Cocommutative Hopf algebras of permutations and trees, with Marcelo Aguiar. Journal of Algebraic Combinatorics, Volume 22, Number 4, pp. 451--470.
10	Combinatorial Hopf Algebras and generalized Dehn-Sommerville relations, with Marcelo Aguiar and Nantel Bergeron, Compositio Mathematica, 142, January 2006, pp. 1-30.
11	Structure of the Loday-Ronco Hopf algebra of trees, with Marcelo Aguiar, Journal of Algebra, Volume 295, Issue 2 , 15 January 2006, Pages 473-511
12	Quiver Coefficients are Schubert Structure Constants, with Anders Buch and Alex Yong, Mathematics Research Letters, Volume 12, Issue 4, (2005) 567-574.
13	Structure of the Malvenuto-Reutenauer Hopf algebra of permutations, with Marcelo Aguiar, Advances in Mathematics 191, (2005), 225--275.
14	Skew Schubert polynomials, with Cristian Lenart, Proc. Amer. Math. Soc., 131 (2003), 3319-3328.
15	A Pieri-type formula for isotropic flag manifolds, with Nantel Bergeron, Trans. Amer. Math. Soc., 354 No. 7, (2002), 2659-2705.
16	Shifted quasi-symmetric functions and the Hopf algebra of peak functions with Nantel Bergeron, S. Mykytiuk, and S. van Willigenburg, Discrete Math., 256 (2002), 57-66.
17	Skew Schubert functions and the Pieri formula for flag manifolds, with Nantel Bergeron. Trans. Amer. Math. Soc., 354 No. 2, (2002), 651-673.
18	Complementary Algorithms for Tableaux, with Tom Roby, Jeff Stroomer, and Julian West. J. Combin. Th. Ser. A, 96, No. 1, October 2001, 127-161.
19	A sagbi basis for the quantum Grassmannian, with Bernd Sturmfels. J. Pure and Appl. Algebra, 158, 24 April 2001 pp. 347-366.
20	Non-commutative Pieri operators on posets, Nantel Bergeron, S. Mykytiuk, and S. van Willigenburg, J. Combin. Th. Ser. A, Vol. 91, No. 1/2, Aug 2000, pp. 84-110.
21	Pieri-type formulas for maximal isotropic Grassmannians via triple intersections, Colloquium Mathematicum, 82 (1999), pp. 49--63.
22	Hopf algebras and edge-labeled posets, with Nantel Bergeron, Journal of Algebra, 216 (1999), pp. 641-651.
23	A monoid for the Grassmannian Bruhat order, with Nantel Bergeron, European Journal of Combinatorics, 20, (1999), pp. 197-211.
24	Schubert polynomials, the Bruhat order, and the geometry of flag manifolds, with Nantel Bergeron, Duke Math. J., 95, (1998), pp. 373-423. A 16 page supplement. A description of how Table 1 was generated.
25	Pieri's formula via explicit rational equivalence, Canad. J. Math., 46 (1997), pp. 1281-1298. A 5 page supplement.
26	Enumerative geometry for the real Grassmannian of lines in projective space, Duke Math. J., 87, (1997), 59-85. Published version of Ph.D. Thesis. The 8 page supplement.
27	Tableau switching: algorithms and applications, with Georgia Benkart and Jeff Stroomer, J. Combin. Th. Ser. A, 76, (1996), pp. 11-43.
28	Pieri's formula for flag manifolds and Schubert polynomials, Annales de l'Institut Fourier, 46 (1996), pp. 89-110.