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LLT polynomials, chromatic quasisymmetric functions and graphs with cycles
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2018 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 341, no 12, p. 3453-3482Article in journal (Refereed) Published
Abstract [en]

We use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as unicellular LLT polynomials, revealing some parallel structure and phenomena regarding their e-positivity. The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials, giving a new extension of LLT polynomials. Carrying over a lot of the noncircular combinatorics, we prove several statements regarding the e-coefficients of chromatic quasisymmetric functions and LLT polynomials, including a natural combinatorial interpretation for the e-coefficients for the line graph and the cycle graph for both families. We believe that certain e-positivity conjectures hold in all these families above. Furthermore, beyond the chromatic analogy, we study vertical-strip LLT polynomials, which are modified Hall-Littlewood polynomials. 

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2018. Vol. 341, no 12, p. 3453-3482
Keywords [en]
Chromatic quasisymmetric functions, Elementary symmetric functions, LLT polynomials, Orientations, Unit interval graphs, Positivity, Diagonal harmonics
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-238893DOI: 10.1016/j.disc.2018.09.001ISI: 000448496500020Scopus ID: 2-s2.0-85053911752OAI: oai:DiVA.org:kth-238893DiVA, id: diva2:1265917
Note

QC 20181126

Available from: 2018-11-26 Created: 2018-11-26 Last updated: 2018-11-26Bibliographically approved

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Alexandersson, Per

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