Continuing what I started in December, I finally finished making a stellated icosahedron out of 30 Sonobe units. Each Sonobe unit corresponds to an edge of the icosahedron, and interlocks with three others to give the whole thing a remarkable degree of rigidity, even though it’s made completely out of paper. 70 more words

## Tags » Group Theory

#### Riffs and Rotes : 3

Re: R.J. Lipton • Failure Of Unique Factorization

My favorite question in this realm is how much of the linear ordering of the natural numbers is purely combinatorial, where we eliminate all the structure that isn’t purely combinatorial via the doubly recursive factorizations of whole numbers, ending up with two species of graph-theoretic structures that I dubbed Riffs and Rotes. 19 more words

#### Mini: Towers (of extensions) that are Galois

This is fairly random, but I thought I might as well write it down. In general it seems hard to say when a tower of Galois extensions is itself Galois… 127 more words

#### Privilege, Power, and Getting Things Done

Sometimes I’ll be sitting in a group discussing our plans and somebody will say, “Hey, I have an idea! What if we do *this*?” The person looks around to the group for an answer. 928 more words

#### The Drive

It was a pleasant Thursday morning. When I had finally crawled out of bed, she already had breakfast prepared on the table and scolded me for meandering and allowing the food to cool. 1,114 more words

#### Splitting fields of representations of generalized symmetric groups, 8

In this post, we give an example.

Let and let

where is a character of and is an irreducible representation of its stabilizer in , . 128 more words

#### Splitting fields of representations of generalized symmetric groups, 7

In this post, we discover which representations of the generalized symmetric group can be realized over a given abelian extension of .

Let be the representation defined previously, where . 136 more words