In this note, we are interested in the following problem: given a chessboard and a set of dominoes, is it possible to tile our chessboard using the dominoes we have? 825 more words

## Tags » Group Theory

#### A Generalization of Wilson's Theorem (due to Gauss)

John Wilson (1741-1793) was a well-known English mathematician in his time, whose legacy lives on in his eponymous result, *Wilson’s Theorem*. To recall, this is the statement that an integer is prime if and only if… 1,015 more words

#### Relations & Their Relatives : 11

Re: Peirce List Discussion • Jeffrey Brian Downard

In discussing the “combinatorial explosion” of dyadic relations that takes off in passing from a universe of two elements to a universe of three elements, I made the following observation: 200 more words

#### 177

June 26 – 177

In finite geometry, a Fano plane is a finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point. 35 more words

#### Universal acylindrical actions

I’m at a fantastic summer graduate school at MSRI (the Mathematical Sciences Research Institute, a.k.a. “math heaven”) right now and re-met a friend I’d seen at a few earlier conferences. 905 more words

#### Observations about the symmetric groups

Recall that the nth symmetric group consists of all permutations of the set {1,…,n}.

**An easier way to multiply elements.** Let’s use (1 2)(2 3) again and see, working left to right, where each number is sent. 1,334 more words

#### Scientific American article about finite simple groups

For those of you who are a bit rusty: a finite group is a group that has a finite number of elements. A simple group is one that has no proper non-trivial normal subgroups (that is, only the identity and the whole group are normal subgroups). 140 more words