10 citations · 16 across the 7 of their papers we have counts for
10 papers · 1 filter
Parking with Frustrated Drivers
Joshua Hallam, Jenson Molebash, Chris Porter
Imagine there are cars lined up along a one-way street containing spots. Each car contains a group of friends, including a reluctant driver. Each car has a preferred spot a…
Whitney Twins, Whitney Duals, and Operadic Partition Posets
Rafael S. González D'León, Joshua Hallam, Yeison A. Quiceno D
We say that a pair of nonnegative integer sequences is Whitney-realizable if there exists a poset for which (the absolute values) of the…
Gorenstein braid cones and crepant resolutions
Joshua Hallam, John Machacek
To any poset , we associate a convex cone called a braid cone. We also associate a fan and study the toric varieties the cone and fan define. The fan always defines a smooth tor…
The Noncrossing Bond Poset of a Graph
C. Matthew Farmer, Joshua Hallam, Clifford Smyth
The partition lattice and noncrossing partition lattice are well studied objects in combinatorics. Given a graph on vertex set , its bond lattice, , is t…
The Whitney Duals of a Graded Poset
Rafael S. González D'León, Joshua Hallam
We introduce the notion of a \emph{Whitney dual} of a graded poset. Two posets are Whitney duals to each other if (the absolute value of) their Whitney numbers of the first and sec…
Increasing spanning forests in graphs and simplicial complexes
Joshua Hallam, Jeremy L. Martin, Bruce E. Sagan
Let G be a graph with vertex set {1,...,n}. A spanning forest F of G is increasing if the sequence of labels on any path starting at the minimum vertex of a tree of F form an incre…
Dual Immaculate Quasisymmetric Functions Expand Positively into Young Quasisymmetric Schur Functions
Edward E. Allen, Joshua Hallam, Sarah K. Mason
We describe a combinatorial formula for the coefficients when the dual immaculate quasisymmetric functions are decomposed into Young quasisymmetric Schur functions. We prove this u…
Combinatorial Hopf Algebras of Simplicial Complexes
Carolina Benedetti, Joshua Hallam, John Machacek
We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a fa…
Applications of Quotient Posets
Joshua Hallam
In this paper we consider the characteristic polynomial of not necessarily ranked posets. We do so by allowing the rank to be an arbitrary function from the poset to the nonnegativ…
Factoring the characteristic polynomial of a lattice
Joshua Hallam, Bruce E. Sagan
We introduce a new method for showing that the roots of the characteristic polynomial of certain finite lattices are all nonnegative integers. This method is based on the notion of…