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# Category Archives: combinatorics

## Species operations: differentiation

Continuing my series describing my new combinatorial species library, today we’ll take a look at the operation of differentiation. You may remember that the Species type class has an Algebra.Differential constraint, which, as I previously explained, transitively implies an Algebra.Ring … Continue reading

Posted in combinatorics, haskell, math
Tagged combinatorial species, combinatorics, differentiation
1 Comment

## Primitive species and species operations, part II

In my previous post, I began describing the primitive species and species operations supported by my combinatorial species library; we looked at the ring structure on species, that is, the primitive species and , and the operations of species sum … Continue reading

Posted in combinatorics, haskell, math
Tagged combinatorial species, combinatorics, cycles, sets, singletons
2 Comments

## Primitive species and species operations

In this second post about my new combinatorial species library, I plan to begin writing about the species DSL itself: what are the primitive combinatorial species and the primitive operations on species? (The first post described the concept of combinatorial … Continue reading

Posted in combinatorics, haskell, math
Tagged combinatorial species, combinatorics, DSL, primitives
3 Comments

## Introducing Math.Combinatorics.Species!

I have just uploaded to Hackage version 0.1 of the species package, a Haskell library for computing with combinatorial species. Much like David Amos’s great series of posts introducing his Haskell for Maths library, I plan to write a series … Continue reading

Posted in combinatorics, haskell, math, projects
Tagged combinatorial species, combinatorics
14 Comments

## The Poisson distribution and Stirling numbers

While working on an assignment for my machine learning class, I rediscovered the fact that if X is a random variable from a Poisson distribution with parameter , then where denotes a Stirling number of the second kind. (I actually … Continue reading

Posted in combinatorics, grad school, learning, math
Tagged Bell numbers, moments, Poisson, Stirling numbers
2 Comments

## Higher-dimensional enumeration

The other day in the #haskell IRC channel, some of us were playing around with generalizing Haskell list enumeration syntax: Prelude> [1..5] [1,2,3,4,5] First, we defined the (…) operator to perform enumeration, so it can be partially applied. (Unfortunately, we … Continue reading

Posted in combinatorics, haskell
Tagged binomial, enumeration, generalization, haskell, non-regular types, simplex
6 Comments