2 citations · 5 across the 18 of their papers we have counts for
24 papers
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…
Finite noncommutative coinvariant algebras
Farid Aliniaeifard, Nantel Bergeron, Huilan Li +1
We study quotients of free associative algebras by the two-sided ideals generated by positive-degree symmetric, quasisymmetric, or free quasisymmetric polynomials. Free quasisymmet…
How to Use Deep Learning to Identify Sufficient Conditions: A Case Study on Stanley's -Positivity
Farid Aliniaeifard, Shu Xiao Li
In a study, published in Nature, researchers from DeepMind and mathematicians demonstrated a general framework using machine learning to make conjectures in pure mathematics. Here,…
The peak algebra in noncommuting variables
Farid Aliniaeifard, Shu Xiao Li
The well-known descent-to-peak map for the Hopf algebra of quasisymmetric functions, , and the peak algebra were originally defined by Stembr…
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…
Chromatic quasisymmetric functions of the path graph
Farid Aliniaeifard, Shamil Asgarli, Maria Esipova +3
We show that the chromatic quasisymmetric function (CQF) of a labeled path graph on vertices is not symmetric unless the labeling is the natural labeling or its…
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…
Hopf structures in the representation theory of direct products
Farid Aliniaeifard, Nathaniel Thiem
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure…
Deletion-contraction for a unified Laplacian and applications
Farid Aliniaeifard, Victor Wang, Stephanie van Willigenburg
We define a graph Laplacian with vertex weights in addition to the more classical edge weights, which unifies the combinatorial Laplacian and the normalised Laplacian. Moreover, we…
Extending the descent-to-peak map and its applications
Farid Aliniaeifard, Shu Xiao Li
The descent-to-peak map serves as a bridge between algebra and combinatorics. We use it as a tool for proving the equidistribution of peak and valley sets of standard Young tableau…
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…
Extended chromatic symmetric functions and equality of ribbon Schur functions
Farid Aliniaeifard, Victor Wang, Stephanie van Willigenburg
We prove a general inclusion-exclusion relation for the extended chromatic symmetric function of a weighted graph, which specializes to (extended) -deletion, and we give two met…
A categorification of the Malvenuto--Reutenauer algebra via a tower of groups
Farid Aliniaeifard, Nathaniel Thiem
There is a long tradition of categorifying combinatorial Hopf algebras by the modules of a tower of algebras (or even better via the representation theory of a tower of groups). Fr…
Pattern groups and a poset based Hopf monoid
Farid Aliniaeifard, Nathaniel Thiem
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying repr…
The structure of normal lattice supercharacter theories
Farid Aliniaeifard, Nathaniel Thiem
The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wis…
Stable set polytopes and their 1-skeleta
Farid Aliniaeifard, Carolina Benedetti, Nantel Bergeron +2
We characterize the edges of two classes of -polytopes. The first class corresponds to the stable set polytope of a graph and includes chain polytopes of posets, some inst…
Theta maps for combinatorial Hopf algebras
Farid Aliniaeifard, Shu Xiao Li
There is a very natural and well-behaved Hopf algebra morphism from quasisymmetric functions to peak algebra, which we call it Theta map. This paper focuses on generalizing the pea…
Positive Self-Dual Hopf Algebras of Galois Characters
Farid Aliniaeifard, Shawn Burkett
By using the action of certain Galois groups on complex irreducible characters and conjugacy classes, we define the Galois characters and Galois classes. We will introduce a set of…
Supercharacters for Normal Supercharacter Theory
Farid Aliniaeifard
In order to find a tractable theory to substitute for the wild character theory of the group of unipotent upper-triangular matrices over a finite field ,…
Normal Supercharacter Theory
Farid Aliniaeifard
There are two main constructions of supercharacter theories for a group . The first, defined by Diaconis and Isaacs, comes from the action of a group via automorphisms on…
Noetherian Rings Whose Annihilating-Ideal Graphs Have finite Genus
Farid Aliniaeifard, Mahmood Behboodi, Yuanlin Li
Let be a commutative ring and be the set of ideals with non-zero annihilators. The annihilating-ideal graph of is defined as the graph with v…
Rings Whose Annihilating-Ideal Graphs Have Positive Genus
Farid Aliniaeifard, Mahmood Behboodi
Let be a commutative ring and be the set of ideals with non-zero annihilators. The annihilating-ideal graph of is defined as the graph with t…