A Common Generalization to Theorems on Set Systems with L-intersections

In this paper, we provide a common generalization to the well-known Erdös.Ko.Rado Theorem, Frankl.Wilson Theorem, Alon.Babai.Suzuki Theorem, and Snevily Theorem on set systems with L-intersections. As a consequence, we derive a result which strengthens substantially the well-known theorem on set systems with k-wise L-intersections by Füredi and Sudakov [J. Combin. Theory, Ser. A, 105, 143.159 (2004)]. We will also derive similar results on L-intersecting families of subspaces of an n-dimensional vector space over a finite field F q , where q is a prime power.