Hello, wrong number At the heart of machine learning are patterns, and patterns are all about counting, so it's important to make sure we are counting the correct items in the correct way.

We know that there are n! permutations of n elements; we have seen this fact when e.g. proving lower bounds on comparison sorting and the brute-force algorithm for solving the Travelling Salesman ...

In the computation of scattering amplitudes, we most often use master integral bases which satisfy 'uniform transcendentality'. These bases are supplied for only one permutation of a given family, so ...

Group H( new Subgroup( S8, {{1,2,3,0,4,5,6,7},{0,1,2,3,5,6,7,4}} ) ); Group I( new Subgroup( S8, {{1,2,3,0,4,5,6,7},{0,1,2,3,5,6,7,4},{4,5,6,7,0,1,2,3}} ) ); ...

We consider producing permutations and combinations in lexicographical order. Except for the array that holds the combinatorial object, we require only O(1) extra storage. The production of the next ...