# Tag Archives: species

## A (work in progress) translation of Joyal’s original paper on species

tl;dr: I’m working on an English translation, with additional commentary, of Joyal’s 1981 paper introducing the concept of combinatorial species. Collaboration and feedback welcome! Back when I was writing my PhD thesis on combinatorial species, I was aware that André … Continue reading

Posted in combinatorics, projects, species, writing | | 6 Comments

## Signed sets and ballots and naturality

This is blog post #3 in a series on signed sets and ballots (the previous posts are here and here). Naturality, isomorphism, and equipotence When are two species isomorphic? Since species are, by definition, functors , the obvious answer is … Continue reading

Posted in combinatorics, math, species | | 2 Comments

## Signed sets and ballots, part 2

Recall, from my previous post, that our goal is to find a combinatorial proof showing the correspondence between signed sets and signed ballots, where a signed set is just a set of elements, considered positive or negative according to the … Continue reading

Posted in combinatorics, math, species | | 1 Comment

## Signed sets and ballots, part 1

The other day, Anders Claesson wrote a very nice blog post explaining a more combinatorial way to understand multiplicative inverses of virtual species (as opposed to the rather algebraic way I explained it in my previous post). In the middle … Continue reading

Posted in combinatorics, math, species | | 2 Comments

## Virtual species suffice

Over six years ago, I wrote a post explaining how virtual species are defined. Ever since then (time flies!) I’ve been meaning to write a follow-up post explaining a bit more about virtual species and how they actually suffice to … Continue reading

Posted in combinatorics | Tagged , | 23 Comments

## The Species of Bracelets

Summary: The species package now has support for bracelets, i.e. equivalence classes of lists up to rotation and reversal. I show some examples of their use and then explain the (very interesting!) mathematics behind their implementation. I recently released a … Continue reading

Posted in combinatorics, haskell, math, species | | 5 Comments

## Crystal Ball Connection Patterns via Species and Generating Functions

A couple weeks ago, Denise posted Puzzle: Crystal Ball Connection Patterns on her blog, Let’s Play Math. I had fun playing with it and thought I would demonstrate how to apply some high-powered combinatorial techniques to it (probably not what … Continue reading

Posted in combinatorics, haskell, math, species | | 1 Comment

tl;dr: Read a draft of my thesis and send me your feedback by September 9! Over the past year I’ve had several people say things along the lines of, “let me know if you want me to read through your … Continue reading

| Tagged , , , , | 15 Comments

## Species subtraction made simple

> {-# OPTIONS_GHC -fno-warn-missing-methods #-} > module Virtual where > > import Control.Applicative > import Test.QuickCheck Yesterday on #haskell, augur asked me to explain how subtraction works for combinatorial species. (For an introduction to species, see my paper from the … Continue reading

Posted in combinatorics, haskell | | 15 Comments

## Back from Baltimore

I’m finally back in Philly after attending ICFP, the Haskell Symposium, and the Haskell Implementors’ Workshop in Baltimore. I enjoyed meeting every person I met, so if I met you please feel free to instantiate the universal quantifier. Here’s a … Continue reading