@article{chromhesssplitting, Author = {Abreu, A. and Nigro, A.}, Eprint = {2304.10644}, Eprinttype = {arXiv}, Title = {Splitting the cohomology of Hessenberg varieties and $e$-positivity of chromatic symmetric functions}, Year = {2023}} @article{lltunicellepos, Author = {Alexandersson, P.}, Journal = {J. Algebraic Combin.}, Page = {299--325}, Title = {LLT polynomials, elementary symmetric functions and melting lollipops}, Volume = {53}, Year = {2021}} @article{csfvertex, Author = {Aliniaeifard, F. and Wang, V. and van Willigenburg, S.}, Eprint = {2108.04850}, Eprinttype = {arXiv}, Title = {The chromatic symmetric function of a graph centred at a vertex}, Year = {2021}} @article{chromquasipower, Author = {Athanasiadis, C.}, Journal = {Electron. J. of Combin.}, Number = {P2.7}, Title = {Power sum expansion of chromatic quasisymmetric functions}, Volume = {22}, Year = {2015}} @article{dothessenberg, Author = {Brosnan, P. and Chow, T.}, Journal = {Adv. in Math.}, Number = {10}, Title = {Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties}, Volume = {329}, Year = {2015}} @article{chrombounce3, Author = {Cho, S. and Hong, J.}, Journal = {Electron. J. Combin.}, Number = {2.19}, Title = {Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3}, Volume = {29}, Year = {2022}} @article{chromhessequi, Author = {Cho, S. and Hong, J. and Lee, E.}, Journal = {Adv. Math.}, Number = {109018}, Title = {Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties}, Volume = {423}, Year = {2023}} @article{chromhecke, Author = {Clearman, S. and Hyatt, M. and Shelton, B. and Skandera, M.}, Journal = {Electron. J. of Combin.}, Title = {Evaluation of Hecke algebra traces at Kazhdan--Lusztig basis elements}, Volume = {23}, Year = {2016}} @article{chromqrook, Author = {Colmenarejo, L. and Morales, A. and Panova, G.}, Journal = {European J. Combin.}, Title = {Chromatic symmetric functions of Dyck paths and $q$-rook theory}, Volume = {107}, Year = {2023}} @article{extendedchromsym, Author = {Crew, L. and Spirkl, S.}, Journal = {Eur. J. Comb.}, Title = {A Deletion-Contraction Relation for the Chromatic Symmetric Function}, Volume = {89}, Year = {2020}} @article{trilad, Author = {Dahlberg, S.}, Eprint = {1811.04885}, Eprinttype = {arXiv}, Title = {Triangular ladders $P_{d,2}$ are $e$-positive}, Year = {2018}} @article{eposclawcon, Author = {Dahlberg, S. and Foley, A. and van Willigenburg, S.}, Journal = {J. Eur. Math. Soc.}, Page = {2673--2696}, Title = {Resolving Stanley's $e$-positivity of claw-contractible-free graphs}, Volume = {22}, Year = {2020}} @article{chromspostrees, Author = {Dahlberg, S. and She, A. and van Willigenburg, S.}, Journal = {J. Combin. Theory Ser. A}, Title = {Chromatic posets}, Volume = {184}, Year = {2021}} @article{lollilari, Author = {Dahlberg, S. and van Willigenburg, S.}, Journal = {SIAM J. Discrete Math.}, Page = {1029--1039}, Title = {Lollipop and lariat symmetric functions}, Volume = {32}, Year = {2018}} @article{chromposnsym, Author = {Dahlberg, S. and van Willigenburg, S.}, Journal = {Adv. in Appl. Math.}, Title = {Chromatic symmetric functions in noncommuting variables revisited}, Volume = {112}, Year = {2020}} @article{eposclasses, Author = {Foley, A. and Hoang, C. and Merkel, O.}, Journal = {Elec. J. of Combin.}, Number = {P3.51}, Title = {Classes of graphs with $e$-positive chromatic symmetric function}, Volume = {26}, Year = {2019}} @article{chrompos31, Author = {Gasharov, V.}, Journal = {Discrete Math.}, Page = {193--197}, Title = {Incomparability graphs of $(3+1)$-free posets are $s$-positive}, Volume = {157}, Year = {1996}} @article{chromnsym, Author = {Gebhard, D. and Sagan, B.}, Journal = {J. Algebr. Comb.}, Title = {A chromatic symmetric function in noncommuting variables}, Volume = {13}, Year = {2001}} @article{stanstemreduction, Author = {Guay-Paquet, M.}, Eprint = {1306.2400}, Eprinttype = {arXiv}, Title = {A modular law for the chromatic symmetric functions of $(3+1)$-free posets}, Year = {2013}} @article{stanstemhess, Author = {Harada, M. and Precup, M.}, Journal = {Algebr. Comb.}, Page = {1059--1108}, Title = {The cohomology of abelian Hessenberg varieties and the Stanley--Stembridge conjecture}, Volume = {2}, Year = {2019}} @article{lltunicellschur, Author = {Huh, J. and Nam, S. and Yoo, M.}, Journal = {Discrete Math.}, Title = {Melting lollipop chromatic quasisymmetric functions and Schur expansion of unicellular LLT polynomials}, Volume = {343}, Year = {2020}} @article{chromtwoparthook, Author = {Hwang, B.-H.}, Eprint = {2208.09857}, Eprinttype = {arXiv}, Title = {Chromatic quasisymmetric functions and noncommutative $P$-symmetric functions}, Year = {2022}} @article{chrombasis, Author = {Sagan, B. and Tom, F.}, Journal = {In preparation}, Title = {Chromatic symmetric functions and change of basis}, Year = {2024}} @article{chromquasihessenberg, Author = {Shareshian, J. and Wachs, M.}, Journal = {Configuration Spaces}, Title = {Chromatic quasisymmetric functions and Hessenberg varieties}, Year = {2012}} @article{chromposquasi, Author = {Shareshian, J. and Wachs, M.}, Journal = {Adv. Math.}, Page = {497--551}, Title = {Chromatic quasisymmetric functions}, Year = {2016}} @article{chromsym, Author = {Stanley, R.}, Journal = {Adv. Math.}, Page = {166--194}, Title = {A symmetric function generalization of the chromatic polynomial}, Volume = {111}, Year = {1995}} @article{stanstem, Author = {Stanley, R. and Stembridge, J.}, Journal = {J. Combin. Theory Ser. A}, Page = {261--279}, Title = {On immanants of Jacobi--Trudi matrices and permutations with restricted position}, Volume = {62}, Year = {1993}} @article{foresttriples, Author = {Tom, F.}, Journal = {In preparation}, Title = {A signed $e$-expansion of the chromatic symmetric function and some new $e$-positive graphs}, Year = {2024}} @article{cyclechordepos, Author = {Wang, D. and Wang, M.}, Eprint = {2112.06679}, Eprinttype = {arXiv}, Title = {Two cycle-chord graphs are $e$-positive}, Year = {2021}} @article{somepos, Author = {Wang, D. and Wang, M.}, Eprint = {2112.06619}, Eprinttype = {arXiv}, Title = {The $e$-positivity and Schur positivity of the chromatic symmetric functions of some trees}, Year = {2021}} @article{chrominvkostka, Author = {Wang, S.}, Eprint = {2210.07567}, Eprinttype = {arXiv}, Title = {The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix}, Year = {2022}}