منابع مشابه
Dense admissible sequences
A sequence of integers in an interval of length x is called admissible if for each prime there is a residue class modulo the prime which contains no elements of the sequence. The maximum number of elements in an admissible sequence in an interval of length x is denoted by %∗(x). Hensley and Richards showed that %∗(x) > π(x) for large enough x. We increase the known bounds on the set of x satisf...
متن کاملDense Admissible Sets
Call a set of integers {b1, b2, . . . , bk} admissible if for any prime p, at least one congruence class modulo p does not contain any of the bi. Let ρ ∗(x) be the size of the largest admissible set in [1, x]. The Prime k-tuples Conjecture states that any for any admissible set, there are infinitely many n such that n+b1, n+b2, . . . n+bk are simultaneously prime. In 1974, Hensley and Richards ...
متن کاملPosets from Admissible Coxeter Sequences
We study the equivalence relation on the set of acyclic orientations of an undirected graph Γ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in tur...
متن کاملOn Cobweb Admissible Sequences - The Production Theorem
In this note further clue decisive observations on cobweb admissible sequences are shared with the audience. In particular an announced proof of the Theorem 1 (by Dziemia´nczuk) from [1] announced in India-Kolkata-December 2007 is delivered here. Namely here and there we claim that any cobweb admissible sequence F is at the point product of primary cobweb admissible sequences taking values one ...
متن کاملDENSE INFINITE Bh SEQUENCES
For h = 3 and h = 4 we prove the existence of infinite Bh sequences B with counting function B(x) = x √ (h−1)2+1−(h−1)+o(1). This result extends a construction of I. Ruzsa for B2 sequences.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2001
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-01-01348-5