User Portlet
Featured Contributor
Brad Klee
Wolfram Research
LOCATION: https://www.inaturalist.org/people/2678305
INTERESTS IN JOBS & NETWORKING:
ABOUT ME:
My introduction to the Wolfram community happened at Curry College, where I studied with Wolfram Summer School. Subsequently I extended my interest in primitive recursive functions to function programming and combinatory logic by working a few problems from Smullyan's "To Mock a Mockingbird". Here is a short program for listing all function compositions and computing the Catalan numbers:
RootedTrees[0] = {F[]}; RootedTrees[N_] := Union@Flatten[ Flatten[Outer[F, Sequence @@ (# /. n_Integer :> RootedTrees[n - 1]), 1]] & /@ Flatten[Permutations /@ IntegerPartitions[N], 1], 1]
Ouput, Count, and Test:
Flatten[RootedTrees /@ Range[0, 5]] Out[]= {F[], F[F[]], F[F[F[]]], F[F[], F[]], F[F[F[F[]]]], F[F[F[], F[]]], F[F[], F[F[]]], F[F[F[]], F[]], F[F[], F[], F[]], F[F[F[F[F[]]]]], F[F[F[F[], F[]]]], F[F[F[], F[F[]]]], F[F[F[F[]], F[]]], F[F[F[], F[], F[]]], F[F[], F[F[F[]]]], F[F[], F[F[], F[]]], F[F[F[]], F[F[]]], F[F[F[F[]]], F[]], F[F[F[], F[]], F[]], F[F[], F[], F[F[]]], F[F[], F[F[]], F[]], F[F[F[]], F[], F[]], F[F[], F[], F[], F[]], F[F[F[F[F[F[]]]]]], F[F[F[F[F[], F[]]]]], F[F[F[F[], F[F[]]]]], F[F[F[F[F[]], F[]]]], F[F[F[F[], F[], F[]]]], F[F[F[], F[F[F[]]]]], F[F[F[], F[F[], F[]]]], F[F[F[F[]], F[F[]]]], F[F[F[F[F[]]], F[]]], F[F[F[F[], F[]], F[]]], F[F[F[], F[], F[F[]]]], F[F[F[], F[F[]], F[]]], F[F[F[F[]], F[], F[]]], F[F[F[], F[], F[], F[]]], F[F[], F[F[F[F[]]]]], F[F[], F[F[F[], F[]]]], F[F[], F[F[], F[F[]]]], F[F[], F[F[F[]], F[]]], F[F[], F[F[], F[], F[]]], F[F[F[]], F[F[F[]]]], F[F[F[]], F[F[], F[]]], F[F[F[F[]]], F[F[]]], F[F[F[F[F[]]]], F[]], F[F[F[F[], F[]]], F[]], F[F[F[], F[]], F[F[]]], F[F[F[], F[F[]]], F[]], F[F[F[F[]], F[]], F[]], F[F[F[], F[], F[]], F[]], F[F[], F[], F[F[F[]]]], F[F[], F[], F[F[], F[]]], F[F[], F[F[]], F[F[]]], F[F[], F[F[F[]]], F[]], F[F[], F[F[], F[]], F[]], F[F[F[]], F[], F[F[]]], F[F[F[]], F[F[]], F[]], F[F[F[F[]]], F[], F[]], F[F[F[], F[]], F[], F[]], F[F[], F[], F[], F[F[]]], F[F[], F[], F[F[]], F[]], F[F[], F[F[]], F[], F[]], F[F[F[]], F[], F[], F[]], F[F[], F[], F[], F[], F[]]} {#, SameQ[#, CatalanNumber[#] & /@ Range[10]] } &@(Length@RootedTrees[#] & /@ Range[10]) Out[]= {{1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796}, True}
STAFF PICKS:
- A period function for anharmonic oscillations
- Blue Tiling
- [GIF] Plotting the Contours of Deformed Hyperspheres
- [GIF] Elaborating on Arrival's Alien Language, Part I., II. & III.
- Isoperiodic time helices and 3D models
- 2D cellular automaton majority classifier on 4 symbols
- Almost indisputable proof of the half-hex cellular automaton
- Note on NKS ch.5 sec.7: Systems Based on Constraints
- The Penrose tiling: casting night and day
- Another model for snowflake growth? maybe.
- Computable proof of Trilobite and Crab
- Converting chess OBJ files to voxels
- A simple multiway example: radioactive decay
- [GiF] Multiway EllipticK in meta chess: dancing pawns
- Mysterious beating heart patterns in totalistic cellular automata
- RandomSierpinskiMaze via Wolfram Function Repository
- Hyperbolic use case for new WFR SubgraphExpand
- Game Trees vs. Game DAGs
- Decently fast SAT solving for wang tiles
- Project L board game analysis
- Analyzing a competitive new method for GenerateTiling
- Finalizing design of DepthFirstSearch: a Backtrack search function
- How difficult is it to Classify SNES map data?
- Taking chess to 2.5 dimensions
- Polyhex snowflakes via FindExactCover
- Fictitious (and reasonable) solutions to simultaneous 3-body collisions
- Angle between two complex 2-vectors
- Intro to event-driven programming: hard square collisions
- Skip-lists: A missing ingredient to WL's Multicomputational paradigm?
- Heart shaped Polyomino Puzzle
- Using (new!) VideoMapList for Pendulum period-energy analysis
- Fixed point analysis of elementary cellular automaton symbol densities