Category Archives: combinatorics

Lightweight invertible enumerations in Haskell

In a previous post I introduced a new Haskell library for enumerations (now on Hackage as simple-enumeration). The Data.Enumeration module defines a type Enumeration a, represented simply by a function Integer -> a which picks out the value of type … Continue reading

Posted in combinatorics, haskell, projects | | 2 Comments

Lightweight, efficiently sampleable enumerations in Haskell

For another project I’m working on, I needed a way to enumerate and randomly sample values from various potentially infinite collections. There are plenty of packages in this space, but none of them quite fit my needs: universe (and related … Continue reading

Posted in combinatorics, haskell, projects | Tagged , , , , | 11 Comments

What’s the Difference? video and slides

At ICFP in St. Louis I presented my paper with Kenny Foner, What’s the Difference? A Functional Pearl on Subtracting Bijections. Many people seemed to enjoy the talk and we got lots of great feedback afterwards. We will probably write up … Continue reading

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New ICFP functional pearl on subtracting bijections

Kenny Foner and I have a paper accepted to ICFP on subtracting bijections. Here’s the basic problem: suppose you have a bijection between two sum types, , and another bijection . Of course and must have the same size, but … Continue reading

Posted in combinatorics, haskell, writing | | 5 Comments

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

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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

Adventures in enumerating balanced brackets

Since I’ve been coaching my school’s ACM ICPC programming team, I’ve been spending a bit of time solving programming contest problems, partly to stay sharp and be able to coach them better, but also just for fun. I recently solved … Continue reading

Posted in combinatorics, haskell | Tagged , , , | 4 Comments