Tag Archives: bijection

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 | Tagged , , , , , , , | Leave a 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 | Tagged , , , , , , | 1 Comment

Pan-Galactic Division in Haskell

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

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 , , , , | 5 Comments