Geodesic
Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3
Soojin Cho1 ; Jaehyun Hong2
1Ajou University
2Center for Complex Geometry, Institute for Basic Science (IBS)
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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We give a proof of the Stanley-Stembridge conjecture on chromatic symmetric functions for the class of all unit interval graphs with independence number 3. That is, we show that the chromatic symmetric function of the incomparability graph of a unit interval order in which the length of a chain is at most 3 is positively expanded as a linear sum of elementary symmetric functions.
DOI : 10.37236/10843
Classification : 05E05, 05C15, 05C25
Mots-clés : Stanley-Stembridge conjecture, chromatic symmetric function

Soojin Cho  1   ; Jaehyun Hong  2

1 Ajou University
2 Center for Complex Geometry, Institute for Basic Science (IBS) 
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     title = {Positivity of chromatic symmetric functions associated with {Hessenberg} functions of bounce number 3},
     journal = {The electronic journal of combinatorics},
     year = {2022},
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     number = {2},
     doi = {10.37236/10843},
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Soojin Cho; Jaehyun Hong. Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10843

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