Technical Note—Further Necessary Conditions for the Existence of a Solution to the Multi-Index Problem

This note gives three new sets of necessary conditions for the existence of a solution to the multi-index problem. One includes as subsets all of the Haley conditions, and all of the 1967 Morávek and Vlach conditions; the second includes as subsets the 1967 Morávek and Vlach conditions; while the third includes as subsets both the first and second new sets of conditions.