13 citations · 30 across the 16 of their papers we have counts for
36 papers
Powers of matrices with all principal minors equal to 1
Darij Grinberg
We say that a square matrix is \emph{-principled} if all its principal minors are equal to . We show that over any well-behaved ring, any power of a -principled…
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…
On the principal minors of the powers of a matrix
Darij Grinberg
We show that if is an -matrix, then the diagonal entries of each power are uniquely determined by the principal minors of , and can be written as universa…
The path-missing and path-free complexes of a directed graph
Darij Grinberg, Lukas Katthän, Joel Brewster Lewis
We study two simplicial complexes arising from a directed graph with two chosen vertices and : the *path-free complex*, consisting of all subsets $F \subseteq E…
Proof of a conjecture of Bergeron, Ceballos and Labbé
Darij Grinberg, Alexander Postnikov
The reduced expressions for a given element of a Coxeter group can be regarded as the vertices of a directed graph ; its arcs correspond to the braid m…
Double posets and the antipode of QSym
Darij Grinberg
A quasisymmetric function is assigned to every double poset (that is, every finite set endowed with two partial orders) and any weight function on its ground set. This generalizes…