Tag Archives: bijection

Lightweight invertible enumerations in Haskell

Posted on July 5, 2019 by Brent

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 | Tagged , , , , , , | 2 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

Pan-Galactic Division in Haskell

Posted on May 12, 2015 by Brent

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 →

Posted in haskell, math, species | Tagged , , , , , , , , , | 6 Comments

Combinatorial species definition

Posted on November 20, 2012 by Brent

Continuing from my previous post, recall that the goal of species is to have a unified theory of containers with labeled1 locations. So, how do we actually specify such things (leaving aside for the moment the question of how we … Continue reading →

Posted in math, species | Tagged , , , , | 7 Comments