9 citations · 37 across the 32 of their papers we have counts for
4 papers · 1 filter
A Generic Numbering System based on Catalan Families of Combinatorial Objects
Paul Tarau
We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work o…
On Two Infinite Families of Pairing Bijections
Paul Tarau
We describe two general mechanisms for producing pairing bijections (bijective functions defined from N x N to N). The first mechanism, using n-adic valuations results in parameter…
Binary Tree Arithmetic with Generalized Constructors
Paul Tarau
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure presen…
A Functional Hitchhiker's Guide to Hereditarily Finite Sets, Ackermann Encodings and Pairing Functions
Paul Tarau
The paper is organized as a self-contained literate Haskell program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmeti…