Stanley–Reisner ring
Imagine you have a bunch of circles made out of little dots. Each dot represents a point on the circle. Now let's say you want to make a shape using these circles. One way to do that is to connect some points on one circle to some points on another circle using lines. These lines will form a shape when you connect all the dots.
This idea of connecting dots from different circles is similar to something called a Stanley-Reisner ring. In a Stanley-Reisner ring, you have a bunch of "faces" (like our circles with dots) and you connect them using "edges" (like our lines connecting the dots).
But there's a catch: not every combination of faces can be connected by an edge. Some combinations just don't make sense, like trying to connect two circles that don't share any points. So you have to follow some rules when connecting the faces with edges.
The Stanley-Reisner ring is named after two mathematicians who came up with this concept. It's used in topology, which is a fancy way of saying the study of shapes and how they can be changed. By using Stanley-Reisner rings, mathematicians can study the different ways that shapes can be connected and what properties they have.
This idea of connecting dots from different circles is similar to something called a Stanley-Reisner ring. In a Stanley-Reisner ring, you have a bunch of "faces" (like our circles with dots) and you connect them using "edges" (like our lines connecting the dots).
But there's a catch: not every combination of faces can be connected by an edge. Some combinations just don't make sense, like trying to connect two circles that don't share any points. So you have to follow some rules when connecting the faces with edges.
The Stanley-Reisner ring is named after two mathematicians who came up with this concept. It's used in topology, which is a fancy way of saying the study of shapes and how they can be changed. By using Stanley-Reisner rings, mathematicians can study the different ways that shapes can be connected and what properties they have.