This package provides optimized functions and flexible combinatorial iterators implemented in C++ for solving problems in combinatorics and computational mathematics. It utilizes the RMatrix class from RcppParallel for thread safety. There are combination/permutation functions with constraint parameters that allow for generation of all results of a vector meeting specific criteria. It is capable of generating specific combinations/permutations which sets up nicely for parallelization as well as random sampling. Gmp support permits exploration where the total number of results is large. Additionally, there are several high performance number theoretic functions that are useful for problems common in computational mathematics.