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# Category Archives: math

## The network reliability problem

Let be a directed graph with vertices and edges . Multiple edges between the same pair of vertices are allowed. For concreteness’ sake, think of the vertices as routers, and the edges as (one-way) connections. Let denote the set of … Continue reading

## A strange representation of Z6

On my other blog I am writing about a proof of the Lucas-Lehmer test, and today in the course of working up some examples I stumbled across this little gem. Let be a monoid, and let denote the subset of … Continue reading

## Catsters guide is complete!

About a year and a half ago I announced that I had started creating a guide to the excellent series of category theory YouTube videos by the Catsters (aka Eugenia Cheng and Simon Willerton). I am happy to report that … Continue reading

## Pan-Galactic Division in Haskell

Summary: given an injective function , it is possible to constructively “divide by ” to obtain an injection , as shown recently by Peter Doyle and Cecil Qiu and expounded by Richard Schwartz. Their algorithm is nontrivial to come up … Continue reading

## Polynomial Functors Constrained by Regular Expressions

I’ve now finished revising the paper that Dan Piponi and I had accepted to MPC 2015; you can find a PDF here: Polynomial Functors Constrained by Regular Expressions Here’s the 2-minute version: certain operations or restrictions on functors can be … Continue reading

Posted in math, writing
Tagged differentiation, dissection, functor, matrices, polynomial, regular expression, semirings
6 Comments