## Abstract

Let n_{o} = 0,n_{1} ≥1...,n_{3} ≥1 be given natural numbers, J_{i}= ∑ t=0 0-1n_{i}+1,..., ∑ t=0 tn_{t} (i=J_{i},...,s) and Π t=0 s E^{n}_{a}=(x(^{t)},...., x(^{1}): n= ∑ i=1 s n_{1} and if rε{lunate} J_{i}, then x(^{u})ε{lunate}{0,..., q_{i}-J} A set R⊆∏_{i}^{3} = 1 E_{aj}^{i2} is said to be (m_{1}, ...,m_{3})-dense (1≤m_{1}≤n) if there exist I_{1}⊆J_{1} such that |L_{1}| = m_{6} (i = 1,...,s) and |L^{(I)}(R)| = ∏_{I}^{5} = q_{l}^{m1} where P^{(I)}(R) is the projection of R on the coordinate axes whose indices lie in I = ∪_{i}^{5} = _{j}L_{1}. In this paper we establish necessary and sufficient conditions for an arbitrary set R⊆∏^{5}_{1} = 1 E_{a1}^{n1} with given |R| to be (m_{1},...,m_{3})-dense.

Original language | English |
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Pages (from-to) | 177-184 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - 1978 |