منابع مشابه
Nowhere 0 mod p dominating sets in multigraphs
Let G be a graph with integral edge weights. A function d : V (G) → Zp is called a nowhere 0 mod p domination function if each v ∈ V satisfies ( d(v) + ∑ u∈N(v) w(u, v)d(u) ) 6= 0 mod p, where w(u, v) denotes the weight of the edge (u, v) and N(v) is the neighborhood of v. The subset of vertices with d(v) 6= 0 is called a nowhere 0 mod p dominating set. It is known that every graph has a nowher...
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For a graph G, a positive integer k, k ≥ 2, and a non-negative integer with z < k and z 6= 1, a subset D of the vertex set V (G) is said to be a non-z (mod k) dominating set if D is a dominating set and for all x ∈ V (G), |N [x] ∩ D| 6≡ z (mod k). For the case k = 2 and z = 0, it has been shown that these sets exist for all graphs. The problem for k ≥ 3 is unknown (the existence for even values...
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Let d > 0 be a squarefree integer and a be an integer, which is not 1 nor a square. Let P(a,d)(x) be the number of primes p x such that p ⌘ 1 mod d and a(p 1)/d ⌘ 1 mod p. Numerical data indicate that the function as approximately equal to a constant multiple of ⇡(x)/(d'(d)) for su ciently large x, where ⇡(x) is the number of primes up to x and '(d) is the Euler-' function. The involved const...
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Alon, Babai and Suzuki proved the following theorem: Let p be a prime and let K , L be two disjoint subsets of {0, 1, . . . , p − 1}. Let |K | = r, |L| = s, and assume r(s − r + 1) ≤ p − 1 and n ≥ s + kr where kr is the maximal element of K . Let F be a family of subsets of an n-element set. Suppose that (i) |F | ∈ K (mod p) for each F ∈ F; (ii) |E ∩ F | ∈ L (mod p) for each pair of distinct se...
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Modular Galois representations ρ : Gal(Q/Q) → GL2(Fp) with cyclotomic determinant arise from elliptic curves for small p. We show that ρ does not necessarily arise from an elliptic curve whose conductor is as small as possible outside p. For p = 3 this disproves a conjecture of J. Lario and A. Rio [8].
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1985
ISSN: 0097-3165
DOI: 10.1016/0097-3165(85)90059-7