5 papers · 1 filter
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…
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…
(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…
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…