### Abstract

We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of the Eulerian polynomials, the one in symmetric function theory deals with a refinement of the chromatic symmetric functions of Stanley, and the one in algebraic geometry deals with Tymoczko’s representation of the symmetric group on the cohomology of the regular semisimple Hessenberg variety of type A. Our purpose is to explore some remarkable connections between these topics.

Original language | English (US) |
---|---|

Title of host publication | Configuration Spaces |

Subtitle of host publication | Geometry, Combinatorics and Topology |

Publisher | Scuola Normale Superiore |

Pages | 433-460 |

Number of pages | 28 |

ISBN (Electronic) | 9788876424311 |

ISBN (Print) | 9788876424304 |

State | Published - Jan 1 2012 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Configuration Spaces: Geometry, Combinatorics and Topology*(pp. 433-460). Scuola Normale Superiore.

**Chromatic quasisymmetric functions and hessenberg varieties.** / Shareshian, John; Galloway, Michelle L.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Configuration Spaces: Geometry, Combinatorics and Topology.*Scuola Normale Superiore, pp. 433-460.

}

TY - CHAP

T1 - Chromatic quasisymmetric functions and hessenberg varieties

AU - Shareshian, John

AU - Galloway, Michelle L

PY - 2012/1/1

Y1 - 2012/1/1

N2 - We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of the Eulerian polynomials, the one in symmetric function theory deals with a refinement of the chromatic symmetric functions of Stanley, and the one in algebraic geometry deals with Tymoczko’s representation of the symmetric group on the cohomology of the regular semisimple Hessenberg variety of type A. Our purpose is to explore some remarkable connections between these topics.

AB - We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of the Eulerian polynomials, the one in symmetric function theory deals with a refinement of the chromatic symmetric functions of Stanley, and the one in algebraic geometry deals with Tymoczko’s representation of the symmetric group on the cohomology of the regular semisimple Hessenberg variety of type A. Our purpose is to explore some remarkable connections between these topics.

UR - http://www.scopus.com/inward/record.url?scp=84928666675&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928666675&partnerID=8YFLogxK

M3 - Chapter

SN - 9788876424304

SP - 433

EP - 460

BT - Configuration Spaces

PB - Scuola Normale Superiore

ER -