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Tag Archives: sets
Types versus sets in math and programming languages
For several years I have been designing and implementing a functional teaching language especially for use in the context of a Discrete Mathematics course. The idea is for students to be exposed to some functional and statically-typed programming early in … Continue reading
Posted in projects, teaching
Tagged foundations, language, math, pedagogy, programming, sets, types
10 Comments
Signed sets and ballots and naturality
This is blog post #3 in a series on signed sets and ballots (the previous posts are here and here). Naturality, isomorphism, and equipotence When are two species isomorphic? Since species are, by definition, functors , the obvious answer is … Continue reading
Posted in combinatorics, math, species
Tagged ballots, bijection, involution, natural, sets, signed, species, virtual
2 Comments
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
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 ballots, bijection, involution, sets, signed, species, virtual
2 Comments
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
blog :: Brent -> [String] 