27 citations · 139 across the 22 of their papers we have counts for
22 papers
Formalizing chip-firing and Riemann--Roch for graphs in Lean 4
Dhyey Dharmendrakumar Mavani, Nathan Pflueger
The Riemann--Roch theorem for graphs, due to Baker and Norine, is a foundational result establishing a powerful analogy between finite graphs and algebraic curves. We describe a co…
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the t…
Transmission permutations and Demazure products in Hurwitz--Brill--Noether theory
Nathan Pflueger
A line bundle on a curve with two marked points can be special in many ways, as measured by the global sections of all of its twists by these points. All of this information is con…
chipfiring: A Python Package for Efficient Mathematical Analysis of Chip-Firing Games on Multigraphs
Dhyey Dharmendrakumar Mavani, Tairan Ji, Nathan Pflueger
This paper presents `chipfiring`, a comprehensive Python package for the mathematical analysis of chip-firing games on finite graphs. The package provides a robust toolkit for defi…
Twice-Marked Banana Graphs & Brill-Noether Generality
Nathan Pflueger, Noah Solomon
We analyze a family of graphs known as banana graphs, with two marked vertices, through the lens of Hurwitz-Brill-Noether theory. As an application, we construct explicit new examp…
An extended Demazure product on integer permutations via min-plus matrix multiplication
Nathan Pflueger
Coxeter groups possess an associative operation, called variously the Demazure, greedy, or 0-Hecke product. For symmetric groups, this product has an amusing formulation, due to Ti…
(Hurwitz-)Brill-Noether general marked graphs via the Demazure product
Nathan Pflueger
This paper gives a novel and compact proof that a metric graph consisting of a chain of loops of torsion order is Brill-Noether general (a theorem of Cools-Draisma-Payne-Robeva…
Linear series with via thrifty lego-building
Nathan Pflueger
The moduli space parameterizing algebraic curves with a linear series of degree and rank has expected relative dimension $ρ= g - (r+…
Weierstrass semigroups from cyclic covers of hyperelliptic curves
Ethan Cotterill, Nathan Pflueger, Naizhen Zhang
The {\it Weierstrass semigroup} of pole orders of meromorphic functions in a point of a smooth algebraic curve is a classical object of study; a celebrated problem of Hurwi…
Versality of Brill-Noether flags and degeneracy loci of twice-marked curves
Nathan Pflueger
A Brill-Noether degeneracy locus is closure in $\Pic^d(C)$ of the locus of line bundles with a specified rank function . These loci generalize the classi…
Combinatorial relations on skew Schur and skew stable Grothendieck polynomials
Melody Chan, Nathan Pflueger
We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued…
Relative Richardson Varieties
Melody Chan, Nathan Pflueger
A Richardson variety in a flag variety is an intersection of two Schubert varieties defined by transverse flags. We define and study relative Richardson varieties, which are define…
The Gieseker-Petri theorem and imposed ramification
Melody Chan, Brian Osserman, Nathan Pflueger
We prove a smoothness result for spaces of linear series with prescribed ramification on twice-marked elliptic curves. In characteristic 0, we then apply the Eisenbud-Harris theory…
Euler characteristics of Brill-Noether varieties
Melody Chan, Nathan Pflueger
We prove an enumerative formula for the algebraic Euler characteristic of Brill-Noether varieties, parametrizing degree d and rank r linear series on a general genus g curve, with…
Weierstrass semigroups on Castelnuovo curves
Nathan Pflueger
We define a class of numerical semigroups S, which we call Castelnuovo semigroups, and study the subvariety of consisting of marked smooth curves with Weierst…
On non-primitive Weierstrass points
Nathan Pflueger
We give an upper bound on the codimension in of the variety of marked curves with a given Weierstrass semigroup. The bound is a combinatorial quantity…
Brill-Noether varieties of k-gonal curves
Nathan Pflueger
We consider a general curve of fixed gonality k and genus g. We propose an estimate for the dimension of the variety of special linear series on C, by solving an analogo…
Special divisors on marked chains of cycles
Nathan Pflueger
We completely describe all Brill-Noether loci on metric graphs consisting of a chain of g cycles with arbitrary edge lengths, generalizing work of Cools, Draisma, Payne, and Robeva…
Genera of Brill-Noether curves and staircase paths in Young tableaux
Melody Chan, Alberto López Martín, Nathan Pflueger +1
In this paper, we compute the genus of the variety of linear series of rank and degree on a general curve of genus , with ramification at least and at two given…
Bitangents of tropical plane quartic curves
Matt Baker, Yoav Len, Ralph Morrison +2
We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For…
On linear series with negative Brill-Noether number
Nathan Pflueger
Brill-Noether theory studies the existence and deformations of curves in projective spaces; its basic object of study is , the moduli space of smooth genus …
Graph reductions, binary rank, and pivots in gene assembly
Nathan Pflueger
We describe a graph reduction operation, generalizing three graph reduction operations related to gene assembly in ciliates. The graph formalization of gene assembly considers thre…