Darij Grinberg

activity

20082026

most citedHopf Algebras in Combinatorics

120 citations · 245 across the 69 of their papers we have counts for

collaborators

Showing 2021Show all

4 papers · 1 filter

math.CO2021

The pre-Pieri rules

Darij Grinberg

Let $R$ be a commutative ring and $n \geq 1$ and $p \geq 0$ two integers. Let $h_{k, i}$ be an element of $R$ for all $k \in Z$ and $i \in [n]$ . For any $α \in Z^{n}$ , we def…

math.CO2021★ 4 cited

On the rank of Hankel matrices over finite fields

Omesh Dhar Dwivedi, Darij Grinberg

Given three nonnegative integers $p, q, r$ and a finite field $F$ , how many Hankel matrices $(x_{i + j})_{0 \leq i \leq p, 0 \leq j \leq q}$ over $F$ have rank $\leq r$ ? Thi…

math.RA2021

On the square of the antipode in a connected filtered Hopf algebra

Darij Grinberg

It is well-known that the antipode $S$ of a commutative or cocommutative Hopf algebra satisfies $S^{2} = id$ (where $S^{2} = S \circ S$ ). Recently, similar results have…

math.CO2021

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 $G = (V, E)$ with two chosen vertices $s$ and $t$ : the *path-free complex*, consisting of all subsets $F \subseteq E…