AN ANALOGUE OF THE HILTON-MILNER THEOREM FOR WEAK COMPOSITIONS
AN ANALOGUE OF THE HILTON-MILNER THEOREM FOR WEAK COMPOSITIONS
Let <TEX>$\mathbb{N}_0$</TEX> be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., <TEX>$P(n,l)=\{(x_1,x_2,{\cdots},x_l){\in}\mathbb{N}^l_0\;:\;x_1+x_2+{\cdots}+x_l=n\}$</TEX>. For any element <TEX>$u=(u_1,u_2,{\cdots},u_l){\in}P(n,l)$</TEX>, denote its ith-coordinate by u(i), i.e., <TEX>$u(i)=u_i$</TEX>. A family <TEX>$A{\subseteq}P(n,l)$</TEX> is said to be t-intersecting if <TEX>${\mid}\{i:u(i)=v(i)\}{\mid}{\geq}t$</TEX> for all <TEX>$u,v{\epsilon}A$</TEX>. …