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Equality of Dual Immaculate Functions Under Automorphisms
Maria Esipova, Stephanie van Willigenburg
The dual immaculate functions are an example of a Schur-like basis in the algebra of quasisymmetric functions. We classify when the image of a dual immaculate function under one of…
A Schur-positivity classification for complete multipartite graphs
Ethan Shelburne, Stephanie van Willigenburg
A graph is Schur-positive if its chromatic symmetric function expands non-negatively in the Schur basis. We determine a full Schur-positivity classification for complete multiparti…
Minimal elements in the skew extended 0-Hecke poset
Nadia Lafrenière, Rosa Orellana, Anna Pun +3
The row-strict 0-Hecke action on standard immaculate skew tableaux was studied by the present authors, who showed that it gives rise to a bounded poset, called the \emph{skew immac…
Schur-positivity for generalized nets
Ethan Shelburne, Stephanie van Willigenburg
A graph is Schur-positive if its chromatic symmetric function expands nonnegatively in the Schur basis. All claw-free graphs are conjectured to be Schur-positive. We introduce a co…
The extra basis in noncommuting variables
Farid Aliniaeifard, Stephanie van Willigenburg
We answer a question of Bergeron, Hohlweg, Rosas, and Zabrocki from 2006 to give a combinatorial description for the coproduct of the x-basis in the Hopf algebra of symmetric funct…