Let Ng(f ) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(f ) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2,3 (Bender and Canf...
A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive intege...