95 citations · 254 across the 26 of their papers we have counts for
32 papers · 1 filter
A universal framework for Hopf algebras in combinatorics
Farid Aliniaeifard, Stephanie van Willigenburg
A universal framework for Hopf algebras in combinatorics provides a unified understanding of combinatorial objects. To establish such a framework, we dualize the theory of combinat…
Equality of skew Schur functions in noncommuting variables
Emma Yu Jin, Stephanie van Willigenburg
The question of classifying when two skew Schur functions are equal is a substantial open problem, which remains unsolved for over a century. In 2022, Aliniaeifard, Li and van Will…
Generalized chromatic functions
Farid Aliniaeifard, Shu Xiao Li, Stephanie van Willigenburg
We define vertex-colourings for edge-partitioned digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. We use our vertex-colourings to define gen…
P-partition power sums
Farid Aliniaeifard, Victor Wang, Stephanie van Willigenburg
We develop the theory of weighted P-partitions, which generalises the theory of P-partitions from labelled posets to weighted labelled posets. We define the related generating func…
The chromatic symmetric function of a graph centred at a vertex
Farid Aliniaeifard, Victor Wang, Stephanie van Willigenburg
We discover new linear relations between the chromatic symmetric functions of certain sequences of graphs and apply these relations to find new families of e-positive unit interval…
Schur functions in noncommuting variables
Farid Aliniaeifard, Shu Xiao Li, Stephanie van Willigenburg
In 2004 Rosas and Sagan asked whether there was a way to define a basis in the algebra of symmetric functions in noncommuting variables, NCSym, having properties analogous to the c…
Slide multiplicity free key polynomials
Soojin Cho, Stephanie van Willigenburg
Schubert polynomials are refined by the key polynomials of Lascoux-Schützenberger, which in turn are refined by the fundamental slide polynomials of Assaf-Searles. In this paper we…
Skew key polynomials and a generalized Littlewood-Richardson rule
Sami Assaf, Stephanie van Willigenburg
Young's lattice is a partial order on integer partitions whose saturated chains correspond to standard Young tableaux, one type of combinatorial object that generates the Schur bas…
Permuted composition tableaux, 0-Hecke algebra and labeled binary trees
Vasu Tewari, Stephanie van Willigenburg
We introduce a generalization of semistandard composition tableaux called permuted composition tableaux. These tableaux are intimately related to permuted basement semistandard aug…
Necessary conditions for Schur-maximality
Foster Tom, Stephanie van Willigenburg
McNamara and Pylyavskyy conjectured precisely which connected skew shapes are maximal in the Schur-positivity order, which says that if is Schur-positive. To…
Resolving Stanley's -positivity of claw-contractible-free graphs
Samantha Dahlberg, Angele Foley, Stephanie van Willigenburg
In Stanley's seminal 1995 paper on the chromatic symmetric function, he stated that there was no known graph that was not contractible to the claw and whose chromatic symmetric fun…
Lollipop and lariat symmetric functions
Samantha Dahlberg, Stephanie van Willigenburg
We compute an explicit -positive formula for the chromatic symmetric function of a lollipop graph, . From here we deduce that there exist countably infinite distinct $e…
Chromatic classical symmetric functions
Soojin Cho, Stephanie van Willigenburg
In this note we classify when a skew Schur function is a positive linear combination of power sum symmetric functions. We then use this to determine precisely when any scalar multi…
Quasisymmetric and noncommutative skew Pieri rules
Vasu Tewari, Stephanie van Willigenburg
In this note we derive skew Pieri rules in the spirit of Assaf-McNamara for skew quasisymmetric Schur functions using the Hopf algebraic techniques of Lam-Lauve-Sottile, and recove…
Chromatic bases for symmetric functions
Soojin Cho, Stephanie van Willigenburg
In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if is a…
Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions
Christine Bessenrodt, Vasu V. Tewari, Stephanie J. van Willigenburg
The classical Littlewood-Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood-Richardson rules for sy…
Noncommutative irreducible characters of the symmetric group and noncommutative Schur functions
Stephanie van Willigenburg
In the Hopf algebra of symmetric functions, Sym, the basis of Schur functions is distinguished since every Schur function is isomorphic to an irreducible character of a symmetric g…
Maximal supports and Schur-positivity among connected skew shapes
Peter R. W. McNamara, Stephanie van Willigenburg
The Schur-positivity order on skew shapes is defined by B \leq A if the difference s_A - s_B is Schur-positive. It is an open problem to determine those connected skew shapes that…
Multiplicity free Schur, skew Schur, and quasisymmetric Schur functions
Christine Bessenrodt, Stephanie van Willigenburg
In this paper we classify all Schur functions and skew Schur functions that are multiplicity free when expanded in the basis of fundamental quasisymmetric functions, termed F-multi…
On (almost) extreme components in Kronecker products of characters of the symmetric groups
Christine Bessenrodt, Stephanie van Willigenburg
Using a recursion formula due to Dvir, we obtain information on maximal and almost maximal components in Kronecker products of characters of the symmetric groups. This is applied t…
Skew quasisymmetric Schur functions and noncommutative Schur functions
Christine Bessenrodt, Kurt Luoto, Stephanie van Willigenburg
Recently a new basis for the Hopf algebra of quasisymmetric functions , called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg.…
Refinements of the Littlewood-Richardson Rule
James Haglund, Kurt W. Luoto, Sarah Mason +1
In the prequel to this paper, we showed how results of Mason involving a new combinatorial formula for polynomials that are now known as Demazure atoms (characters of quotients of…
Quasisymmetric Schur functions
J. Haglund, K. Luoto, S. Mason +1
We introduce a new basis for quasisymmetric functions, which arise from a specialization of nonsymmetric Macdonald polynomials to standard bases, also known as Demazure atoms. Our…
Expressions for Catalan Kronecker Products
Andrew Brown, Stephanie van Willigenburg, Mike Zabrocki
We give some elementary manifestly positive formulae for the Kronecker products s_(d,d) * s_(d+k,d-k) and s_(d,d) * s_(2d-k,1^k). These formulae demonstrate some fundamental proper…