Discrete Mathematics & Theoretical Computer Science |

- 1 Department of Mathematics
- 2 Department of Mathematics [Univ California San Diego]

Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the $\textit{quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the $\textit{row-strict quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through row-strict tableaux. We describe the relationship between this new basis and other known bases for quasisymmetric functions, as well as its relationship to Schur polynomials. We obtain a refinement of the omega transform operator as a result of these relationships.

Source: HAL:hal-01215042v1

Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)

Section: Proceedings

Published on: January 1, 2011

Imported on: January 31, 2017

Keywords: symmetric and quasisymmetric functions,omega operator,Schur functions,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

- Source : OpenAIRE Graph
*PostDoctoral Research Fellowship*; Funder: National Science Foundation; Code: 0603351*Combinatorial Structures for Permutation Enumeration and Macdonald Polynomials*; Funder: National Science Foundation; Code: 0654060

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