1 citations · 2 across the 5 of their papers we have counts for
7 papers
On Kostant's weight -multiplicity formula for
Rebecca E. Garcia, Pamela E. Harris, Marissa Loving +5
The -analog of Kostant's weight multiplicity formula is an alternating sum over a finite group, known as the Weyl group, whose terms involve the -analog of Kostant's partitio…
Beyond Coins, Stamps, and Chicken McNuggets: an Invitation to Numerical Semigroups
Scott Chapman, Rebecca Garcia, Christopher O'Neill
We give a self contained introduction to numerical semigroups, and present several open problems centered on their factorization properties.
The Graph of Critical Pairs of a Crown
Fidel Barrera-Cruz, Rebecca Garcia, Pamela Harris +5
There is a natural way to associate with a poset a hypergraph , called the hypergraph of critical pairs, so that the dimension of is exactly equal to the chromatic numbe…
Gröbner Bases of Neural Ideals
Rebecca Garcia, Luis David García Puente, Ryan Kruse +5
The brain processes information about the environment via neural codes. The neural ideal was introduced recently as an algebraic object that can be used to better understand the co…
Neural Ideals in SageMath
Ethan Petersen, Nora Youngs, Ryan Kruse +3
A major area in neuroscience research is the study of how the brain processes spatial information. Neurons in the brain represent external stimuli via neural codes. These codes oft…
Block Circulant Graphs and the Graphs of Critical Pairs of a Crown
Rebecca E. Garcia, Pamela E. Harris, Bethany Kubik +2
In this paper, we provide a natural bijection between a special family of block circulant graphs and the graphs of critical pairs of the posets known as generalized crowns. In part…
Algebraic and combinatorial aspects of sandpile monoids on directed graphs
Scott Chapman, Rebecca Garcia, Luis David García-Puente +2
The sandpile group of a graph is a well-studied object that combines ideas from algebraic graph theory, group theory, dynamical systems, and statistical physics. A graph's sandpile…