All Questions

I noted a while ago that there is a nice homological formulation using incidence algebra of the Union-closed sets conjecture (https://en.wikipedia.org/wiki/Union-closed_sets_conjecture). It might just ...

For $n \geq 3$ and $r \geq 3$ let $C_{n,r}=(c_{i,j})$ denote the $n \times n$-matrix where $c_{i,j}=1$ for $j=i,\dots,i+r-1$ (we only do this until $i+r-1>n$). So for example for $n=7$ and $r=3$ we ...

(This question can be formulated purely combinatorially in terms of Dyck paths, which is done in the second part of the question. But I am more interested whether this can be explained by some sort of ...

My question comes from learning the paper [BGS96] Koszul duality patterns in representation theory by Beilinson, Ginzburg and Soergel, published in 1996. Let $A=T_{A_0}A_1/\langle R\rangle$ be a ...