Category Archives: combinatorics

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 | Tagged , , , , , | 1 Comment

Readers wanted!

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

Random binary trees with a size-limited critical Boltzmann sampler

Today I’d like to talk about generating random trees. First, some imports and such (this post is literate Haskell). > {-# LANGUAGE GeneralizedNewtypeDeriving #-} > > module BoltzmannTrees where > > import Control.Applicative > import Control.Arrow ((&&&)) > import Control.Lens … Continue reading

Posted in combinatorics, haskell, math, species | Tagged , , , , , | 9 Comments

And now, back to your regularly scheduled combinatorial species

I’ve already mentioned this to people here and there, but haven’t yet announced it publically, so here it is: Stephanie Weirich and I have been awarded a grant from the NSF to study the intersection of combinatorial species and (functional) … Continue reading

Posted in combinatorics, math, writing | Tagged , | 10 Comments

Unordered tuples and type algebra

At Hac Phi a few weekends ago (which, by the way, was awesome), Dan Doel told me about a certain curiosity in type algebra, and we ended up working out a bunch more details together with Gershom Bazerman, Scott Walck, … Continue reading

Posted in combinatorics | Tagged , , , , | 7 Comments

Counting linear lambda terms: choice and correspondence

In my last post, I showed how to write down polymorphic types with numbers of linear inhabitants given by products of factorials and Mersenne numbers, but left open the question of types with five linear inhabitants in particular, and whether … Continue reading

Posted in combinatorics | Tagged , , , , | 1 Comment

Counting linear lambda terms: Mersenne numbers

In a previous post I posed the challenge of coming up with polymorphic types admitting certain numbers of linear inhabitants. (If you didn’t see the previous post and want to puzzle over an interesting lambda-calculus based problem, stop reading now … Continue reading

Posted in combinatorics | 18 Comments