Tag Archives: species

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

Posted on February 13, 2018 by Brent

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 | Tagged , , , , , , | 6 Comments

Signed sets and ballots and naturality

Posted on February 27, 2017 by Brent

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 | Tagged , , , , , , , | 2 Comments

Signed sets and ballots, part 2

Posted on February 24, 2017 by Brent

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 | Tagged , , , , , , , | 1 Comment

Signed sets and ballots, part 1

Posted on February 20, 2017 by Brent

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 | Tagged , , , , , , | 2 Comments

Virtual species suffice

Posted on February 10, 2017 by Brent

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

Posted on July 10, 2015 by Brent

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 | Tagged , , | 5 Comments

Crystal Ball Connection Patterns via Species and Generating Functions

Posted on June 2, 2015 by Brent

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 | Tagged , , , , , | 1 Comment

Readers wanted!

Posted on August 10, 2014 by Brent

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 →

Posted in category theory, combinatorics, diagrams, grad school, math, species, writing | Tagged , , , , | 15 Comments

Species subtraction made simple

Posted on November 24, 2010 by Brent

> {-# 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 | Tagged , , , , , , , | 15 Comments

Back from Baltimore

Posted on October 2, 2010 by Brent

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 →

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