This short note gives an alternative proof of the M-convex intersection theorem, which is one of the central results in discrete convex analysis. This note is intended to provide a direct simpler proof accessible to nonexperts. 1 M-Convex Intersection Theorem The M-convex intersection theorem [3, Theorem 8.17] reads as follows, where V is a nonempty finite set, and Z and R are the sets of integ...

Mg,n ψ1 1 · · ·ψ dn n . Witten-Kontsevich theorem [9, 4] provides a recursive way to compute all these intersection numbers. However explicit and effective recursion formulae for computing intersection indices are still very rare and very welcome. Our n-point function formula [5] computes intersection indices recursively by decreasing the number of marked points. So it is natural to ask whether...