Set Systems with Restricted $t$-wise Intersections Modulo Prime Powers
نویسندگان
چکیده
منابع مشابه
Set Systems with Restricted t-wise Intersections Modulo Prime Powers
We give a polynomial upper bound on the size of set systems with restricted t-wise intersections modulo prime powers. Let t ≥ 2. Let p be a prime and q = p be a prime power. Let L = {l1, l2, . . . , ls} be a subset of {0, 1, 2, . . . , q − 1}. If F is a family of subsets of an n element set X such that |F1 ∩ · · · ∩ Ft| (mod q) ∈ L for any collection of t distinct sets from F and |F | (mod q) /...
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We study set systems satisfying FrankllWilson-type conditions modulo prime powers. We prove that the size of such set systems is polynomially bounded, in contrast with V. Grolmusz's recent result that for non-prime-power moduli, no polynomial bound exists. More precisely we prove the following result. Theorem. Let p be a prime and q= p k. v For all i, j (1i< jm), there exists l (1ls) such that ...
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Let p be a prime and let L = {l1, l2, . . . , ls} and K = {k1, k2, . . . , kr} be two subsets of {0, 1, 2, . . . , p − 1} satisfying max lj < min ki. We will prove the following results: If F = {F1, F2, . . . , Fm} is a family of subsets of [n] = {1, 2, . . . , n} such that |Fi ∩ Fj | (mod p) ∈ L for every pair i 6= j and |Fi| (mod p) ∈ K for every 1 ≤ i ≤ m, then |F| ≤ ( n− 1 s ) + ( n− 1 s− 1...
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Let S be a set of n elements, and let H be a set-system on S, which satisses that the size of any element of H is divisible by m, but the intersection of any two elements of H is not divisible by m. If m is a prime or prime-power, then the famous Frankl{Wilson theorem 3] implies that jHj = O(n m?1), i.e. for xed m, its size is at most polynomial in n. This theorem has numerous applications in c...
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A large variety of problems and results in Extremal Set Theory deal with estimates on the size of a family of sets with some restrictions on the intersections of its members. Notable examples of such results, among others, are the celebrated theorems of Fischer, RayChaudhuri–Wilson and Frankl–Wilson on set systems with restricted pairwise intersections. These also can be considered as estimates...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/255