1
vote
1answer
96 views

Number of 2n-1 equal size partitions up to symmetry

Consider the $K_{2n}$ (or just the set $\{1,\dots,2n\}$) with $S_{2n}$ acting on the vertices. Moreover consider a collection of 2n-1 partitions of the vertices into two equal sized sets (repeated ...
4
votes
2answers
84 views

Automorphisms of a structure as a powerful tool for studying the structure

This is just an arbitrary testimony of an often repeated slogan: "The group of automorphisms of a given structure is often a powerful tool for studying this structure." D. Lascar, On the ...
1
vote
2answers
130 views

What is 3-symmetric drawing of graph

i have searched through internet, but found only paid articles. Need to understand how Petersen graph can be contracted to K33, it says what through deleting the central vertex of 3-symmetric drawig. ...
5
votes
1answer
245 views

Walks of Even Length on a Bipartite Graph

Given a random walk on a simple $d$-regular bipartite graph $G$. The adjacency matrix $A'$ of $G$ may be split into blocks $$ A'=\pmatrix{ 0 &A^T\\ A&0 }, $$ The propagation operator $M=A'/d$ ...
0
votes
1answer
85 views

What is the name of the symmetry of a bracelet transposition?

Take a bracelet with colored beads on it. Normally two bracelets belong to the same equivalence class under rotations and reflections. For an example, consider the bracelet denoted by the word ...
0
votes
1answer
123 views

How to apply the Poincaré formula to a regular n-gon?

I've been trying to solve the following home task: Choose $n$ points ($n\ge 2$) on the circle's circumference and connect them all with each other using chords. In result, the circle is ...