6 citations · 8 across the 17 of their papers we have counts for
17 papers
A lattice path model for the volume of the Monge polytope
William Q. Erickson, Nicholas B. Jones
Monge matrices arise throughout combinatorial optimization and algorithm design; the Monge polytope is the set of Monge matrices lying inside the st…
Homometric subsets of with cardinality 5: classification and enumeration
William Q. Erickson, Nicholas B. Jones
Two subsets of are said to be homometric if they have the same multiset of pairwise cyclic (i.e., Lee) distances. Homometric subsets necessarily have the same cardin…
The Demazure product extended to biwords
William Q. Erickson
The symmetric group (and more generally, any Coxeter group) admits an associative operation known as the Demazure product. In this paper, we first extend the Demaz…
Expected value and a Cayley-Menger type formula for the generalized earth mover's distance
William Q. Erickson
The earth mover's distance (EMD), also known as the 1-Wasserstein metric, measures the minimum amount of work required to transform one probability distribution into another. The E…
The structure and normalized volume of Monge polytopes
William Q. Erickson, Jan Kretschmann
A matrix has the Monge property if for all and . Monge matrices play an important role in combinatorial optimization; for…
Young tableau reconstruction via minors
William Q. Erickson, Daniel Herden, Jonathan Meddaugh +4
The tableau reconstruction problem, posed by Monks (2009), asks the following. Starting with a standard Young tableau , a 1-minor of is a tableau obtained by first deleting…
Palindromicity of the numerator of a statistical generating function
Rebecca Bourn, William Q. Erickson
We prove a conjecture of Bourn and Willenbring (2020) regarding the palindromicity and unimodality of a certain family of polynomials . These recursively defined polynomial…
A Cayley-Menger formula for the earth mover's simplex
William Q. Erickson
The earth mover's distance (EMD) is a well-known metric on spaces of histograms; roughly speaking, the EMD measures the minimum amount of work required to equalize two histograms.…
The sum of all width-one tensors
William Q. Erickson, Jan Kretschmann
This paper generalizes a recent result by the authors concerning the sum of width-one matrices; in the present work, we consider width-one tensors of arbitrary dimensions. A tensor…
The sum of all width-one matrices
William Q. Erickson, Jan Kretschmann
A nonnegative integer matrix is said to be width-one if its nonzero entries lie along a path consisting of steps to the south and to the east. These matrices are important in optim…
Dimension identities, almost self-conjugate partitions, and BGG complexes for Hermitian symmetric pairs
William Q. Erickson, Markus Hunziker
An almost self-conjugate (ASC) partition has a Young diagram in which each arm along the diagonal is exactly one box longer than its corresponding leg. Classically, the ASC partiti…
Klein cordial trees and odd cyclic cordial friendship graphs
William Q. Erickson, Daniel Herden, Jonathan Meddaugh +7
For a graph and an abelian group , a labeling of the vertices of induces a labeling of the edges via the sum of adjacent vertex labels. Hovey introduced the notion of an…
Graphical methods and rings of invariants on the symmetric algebra
Rebecca Bourn, William Q. Erickson, Jeb F. Willenbring
Let be a complex classical group, and let be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to writ…
Enright resolutions encoded by a generating function for Blattner's formula: Type A
William Q. Erickson
Consider the classical action of on a sum of copies of the defining representation and copies of its dual; by Howe duality, the polynomial functions on this sp…
Comparing weighted difference and earth mover's distance via Young diagrams
William Q. Erickson
We consider two natural statistics on pairs of histograms, in which the bins have weights . The difference () between the weighted totals of the his…
Contingency tables and the generalized Littlewood-Richardson coefficients
Mark Colarusso, William Q. Erickson, Jeb F. Willenbring
The Littlewood-Richardson coefficients give the multiplicity of an irreducible polynomial -representation in the tensor product of polynomial represe…
A generalization for the expected value of the earth mover's distance
William Q. Erickson
The earth mover's distance (EMD), also called the first Wasserstein distance, can be naturally extended to compare arbitrarily many probability distributions, rather than only two,…