Pages

Categories
 abstraction AC algorithm announcement applicative art axiom of choice Beeminder Bell numbers BlogLiterately category category theory collaborative editing combinatorial combinatorial species combinatorics constraints constructive cycles darcs data diagrams dissertation drawing DSL EDSL feedback FringeDC functional functional programming functor GHC ghci grad school graphics hackathon Hac φ haskell ICFP isomorphism knowledge library list lists monad Monad.Reader monads monoid monoids multiset music partitions patch theory pedagogy Philadelphia pictures preorder productivity programming QuickCheck reading release species talk text theory translation tutorial typelevel type classes Typeclassopedia types unique UPenn xmonad
Archives
 August 2014 (3)
 June 2014 (2)
 May 2014 (2)
 January 2014 (2)
 October 2013 (1)
 August 2013 (1)
 July 2013 (1)
 May 2013 (1)
 April 2013 (3)
 March 2013 (2)
 January 2013 (2)
 December 2012 (2)
 November 2012 (4)
 October 2012 (3)
 August 2012 (4)
 July 2012 (5)
 June 2012 (1)
 March 2012 (1)
 January 2012 (1)
 November 2011 (4)
 October 2011 (3)
 September 2011 (2)
 August 2011 (2)
 July 2011 (2)
 June 2011 (1)
 May 2011 (6)
 April 2011 (2)
 March 2011 (1)
 February 2011 (3)
 January 2011 (1)
 December 2010 (2)
 November 2010 (3)
 October 2010 (1)
 September 2010 (1)
 August 2010 (3)
 July 2010 (2)
 June 2010 (3)
 May 2010 (3)
 April 2010 (3)
 March 2010 (2)
 February 2010 (1)
 January 2010 (1)
 December 2009 (2)
 October 2009 (3)
 September 2009 (2)
 August 2009 (4)
 July 2009 (7)
 June 2009 (1)
 May 2009 (2)
 April 2009 (1)
 March 2009 (2)
 February 2009 (3)
 January 2009 (3)
 December 2008 (2)
 September 2008 (2)
 August 2008 (1)
 July 2008 (3)
 June 2008 (1)
 April 2008 (4)
 March 2008 (4)
 February 2008 (4)
 January 2008 (2)
 December 2007 (4)
 October 2007 (2)
 September 2007 (2)
 August 2007 (3)
 June 2007 (2)
Top Posts
Blogroll
Fun
Personal
Meta
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
Higherdimensional 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, nonregular types, simplex
6 Comments