9 citations · 24 across the 17 of their papers we have counts for
18 papers
Vector encoding of phylogenetic trees by ordered leaf attachment
Harry Richman, Cheng Zhang, Frederick A. Matsen
As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "orde…
PhyloVAE: Unsupervised Learning of Phylogenetic Trees via Variational Autoencoders
Tianyu Xie, Harry Richman, Jiansi Gao +2
Learning informative representations of phylogenetic tree structures is essential for analyzing evolutionary relationships. Classical distance-based methods have been widely used t…
Principal minors of tree distance matrices
Harry Richman, Farbod Shokrieh, Chenxi Wu
We prove that the principal minors of the distance matrix of a tree satisfy a combinatorial expression involving counts of rooted spanning forests of the underlying tree. This gene…
The family of -floor quotient partial orders
Jeffrey C. Lagarias, David Harry Richman
An approximate divisor order is a partial order on the positive integers that refines the divisor order and is refined by the additive total order. A previous paper…
A Ricci flow on graphs from effective resistance
Aleyah Dawkins, Vishal Gupta, Mark Kempton +4
In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study…
Node resistance curvature in Cartesian graph products
Aleyah Dawkins, Vishal Gupta, Mark Kempton +4
Devriendt and Lambiotte recently introduced the \emph{node resistance curvature}, a notion of graph curvature based on the effective resistance matrix. In this paper, we begin the…
The Möbius function of the poset of triangular numbers under divisibility
Rohan Pandey, Harry Richman
This paper analyzes the Möbius () function defined on the partially ordered set of triangular numbers () under the divisibility relation. We make conjectures o…
Counting two-forests and random cut size via potential theory
Harry Richman, Farbod Shokrieh, Chenxi Wu
We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average c…
Tropical Weierstrass points and Weierstrass weights
Omid Amini, Lucas Gierczak, Harry Richman
In this paper, we study tropical Weierstrass points. These are the analogues for tropical curves of ramification points of line bundles on algebraic curves. For a divisor on a trop…
Lower rational approximations and Farey staircases
David Harry Richman
For a real number , call the -th lower rational approximation of . We study the functions defined by taking the cumulative average of the firs…
The floor quotient partial order
Jeffery C. Lagarias, David Harry Richman
A positive integer is a floor quotient of if there is a positive integer such that . The floor quotient relation defines a partial order on the…
The tropical Manin-Mumford conjecture
David Harry Richman
In analogy with the Manin-Mumford conjecture for algebraic curves, one may ask how a metric graph under the Abel-Jacobi embedding intersects torsion points of its Jacobian. We show…
Counting Tripods on the Torus
Jayadev S. Athreya, David Aulicino, Harry Richman
Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, tripods, on the flat torus. Classical Euclidean geometry turns this into a lattice po…
Derangements and the -adic incomplete gamma function
Andrew O'Desky, David Harry Richman
We introduce a -adic analogue of the incomplete gamma function. We also introduce quantities (-values) associated to a function on natural numbers and prove a new characteriz…
Dilated floor functions having nonnegative commutator II. Negative dilations
Jeffrey C. Lagarias, D. Harry Richman
This paper completes the classification of the set of all real parameter pairs such that the dilated floor functions , $f_β(x) = \lfloor{βx…
The distribution of Weierstrass points on a tropical curve
David Harry Richman
We show that on a metric graph of genus , a divisor of degree generically has Weierstrass points. For a sequence of generic divisors on a metric graph whose degre…
Dilated floor functions having nonnegative commutator I. Positive and mixed sign dilations
Jeffrey C. Lagarias, D. Harry Richman
In this paper and its sequel we classify the set of all real parameter pairs such that the dilated floor functions and $f_β(x) = \lfloor{β…
Dilated Floor Functions That Commute
Jeffrey C. Lagarias, Takumi Murayama, D. Harry Richman
We determine all pairs of real numbers such that the dilated floor functions and commute under composition, i.e., such that $\lfloo…