Years ago, I had a similar need and I consulted TAOCP to find the “standard” algorithm to do so, which is done by a binomial tree. The tree T is defined recursively as T(0) = nil and T(n) = [Cons(0, T(0)), Cons(1, T(1)), ..., Cons(n-1, T(n-1))]. There's no need to construct the tree explicitly; it's just a conceptual formalism that helps formulate an algorithm to traverse the tree.
The text did mention using bitwise operations to do so; in fact it says it presents a “remarkable sequence of seven bitwise operations that will convert any binary number to the lexicographically next t-combination” but I haven't been able to find those seven operations.
Years ago, I had a similar need and I consulted TAOCP to find the “standard” algorithm to do so, which is done by a binomial tree. The tree T is defined recursively as T(0) = nil and T(n) = [Cons(0, T(0)), Cons(1, T(1)), ..., Cons(n-1, T(n-1))]. There's no need to construct the tree explicitly; it's just a conceptual formalism that helps formulate an algorithm to traverse the tree.
The text did mention using bitwise operations to do so; in fact it says it presents a “remarkable sequence of seven bitwise operations that will convert any binary number to the lexicographically next t-combination” but I haven't been able to find those seven operations.