120 citations · 245 across the 69 of their papers we have counts for
7 papers · 1 filter
The Elser nuclei sum revisited
Darij Grinberg
Fix a finite undirected graph and a vertex of . Let be the set of edges of . We call a subset of pandemic if each edge of has at least one endpoint th…
Three variations on the linear independence of grouplikes in a coalgebra
Gérard Duchamp, Darij Grinberg, Vincel Minh
The grouplike elements of a coalgebra over a field are known to be linearly independent over said field. Here we prove three variants of this result. One is a generalization to coa…
Notes on the combinatorial fundamentals of algebra
Darij Grinberg
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, bino…
The Pelletier-Ressayre hidden symmetry for Littlewood-Richardson coefficients
Darij Grinberg
We prove an identity for Littlewood--Richardson coefficients conjectured by Pelletier and Ressayre (arXiv:2005.09877). The proof relies on a novel birational involution defined ove…
Proof of three conjectures on determinants related to quadratic residues
Darij Grinberg, Zhi-Wei Sun, Lilu Zhao
In this paper we confirm three conjectures of Z.-W. Sun on determinants. We first show that any odd integer divides the determinant $$\left|(i^2+dj^2)\left(\frac{i^2+dj^2}n\r…
Petrie symmetric functions
Darij Grinberg
For any positive integer and nonnegative integer , we consider the symmetric function defined as the sum of all monomials of degree that involve onl…