Abstract
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.
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Liu, J.Q., Zhang, S.G. & Xiao, J.M. A Common Generalization to Theorems on Set Systems with L-intersections. Acta. Math. Sin.-English Ser. 34, 1087–1100 (2018). https://doi.org/10.1007/s10114-018-6577-0
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DOI: https://doi.org/10.1007/s10114-018-6577-0
Keywords
- Alon–Babai–Suzuki Theorem
- Erdös–Ko–Rado Theorem
- Frankl–Wilson Theorem
- Snevily Theorem
- multilinear polynomials