Schur positivity and Schur log-concavity

By Thomas Lam, Alexander Postnikov, Pavlo Pylyavskyy. 2005

97 citations recorded by the source corpus.

We prove Okounkov's conjecture, a conjecture of Fomin-Fulton-Li-Poon, and a special case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. We also give an intriguing log-concavity property of Schur functions.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1af51e9659ec4619e42c80c79a3adf0a321efac2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Hugh Thomas
2. Alexander Yong
3. Larry X. W. Wang
4. William Y. C. Chen
5. I. Reiten
6. Lingyan Guo
7. B. Keller
8. Osamu Iyama

In Discrete Mathematics and Combinatorics

1. Hugh Thomas
2. Alexander Yong
3. Arthur L. B. Yang
4. Larry X. W. Wang
5. William Y. C. Chen
6. I. Reiten
7. Lingyan Guo
8. B. Keller

In Geometry and Topology

1. Hugh Thomas
2. Arthur L. B. Yang
3. Larry X. W. Wang
4. Alexander Yong
5. William Y. C. Chen
6. I. Reiten
7. Osamu Iyama
8. B. Keller

Citations in the corpus

• A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus (2007, background): “This conjecture generalizes a theorem in the cohomological case [Lam et al. 2007]; see related work [Okounkov 2003; Fomin et al.”
• Schur positivity and the q-log-convexity of the Narayana polynomials (2008, result): “To this end, we recall a result due to Lam, Postnikov and Pylyavaskyy [18], which was conjectured by Lam and Pylyavaskyy [17].”