Tags on subsets

A new definition of a tag on a subset of a finite set is given. Tags were recently defined in a joint paper of the author and J.S. Chahal. The new definition considerably simplifies the concepts further. Relationship with lexicographic ordering is much more visible. Applications to a general (t,k)(t,k) existence problem which includes the existence conjecture for t-designs or characterizing degree sequences of a k-uniform hypergraphs as particular cases is discussed. Some new necessary inequalities, as well as some sufficient conditions for such existence questions are derived.