Pd,2, which we call triangular ladders, are e-positive. In this extended abstract we summarize our confirmation of this conjecture, which is also an unsolved case of the celebrated (3+1)-free conjecture. Gebhard and Sagan defined chromatic symmetric functions in non-commuting variables that satisfy a deletion-contraction property unlike the chromatic symmetric functions in commuting variables. We prove a new signed combinatorial formula for the chromatic symmetric function of \emph{any} unit interval graph in the basis of elementary symmetric functions. Then we find that triangular ladders are e-positive by very carefully defining a sign-reversing involution on our signed combinatorial formula, which leaves us with certain positive terms and further allows us to expand an already known family of e-positive graphs by Gebhard and Sagan.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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