Abstract
Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur-positive is a long-standing problem in algebraic combinatorics. In this paper we present a general method to construct Schur-positive sets and multisets, based on geometric grid classes and the product operation. Our approach produces many new instances of Schur-positive sets, and provides a broad framework that explains the existence of known such sets that until now were sporadic cases.
| Original language | English |
|---|---|
| Pages (from-to) | 443-454 |
| Number of pages | 12 |
| Journal | Discrete Mathematics and Theoretical Computer Science |
| State | Published - 2016 |
| Event | 28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada Duration: 4 Jul 2016 → 8 Jul 2016 |
Bibliographical note
Publisher Copyright:© 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France
Funding
†Email: [email protected]. Partially supported by grant #280575 from the Simons Foundation and by grant H98230-14-1-0125 from the NSA. ‡Email: [email protected]. Partially supported by Dartmouth’s Shapiro visitors fund.
| Funders | Funder number |
|---|---|
| Simons Foundation | H98230-14-1-0125 |
| National Security Agency |
Keywords
- Arc permutation
- Descent
- Grid class
- Kronecker product
- Quasisymmetric function
- Schur-positivity
- Symmetric group