  We consider the restricted subsets of $\mathbb{N}_n=\{1,2,\ldots,n\}$ with
$q\geq1$ being the largest member of the set $\mathcal{Q}$ of disallowed
differences between subset elements. We obtain new results on various classes
of problem involving such combinations lacking specified separations. In
particular, we find recursion relations for the number of $k$-subsets for any
$\mathcal{Q}$ when $|\mathbb{N}_q-\mathcal{Q}|\leq2$. The results are obtained,
in a quick and intuitive manner, as a consequence of a bijection we give
between such subsets and the restricted-overlap tilings of an $(n+q)$-board (a
linear array of $n+q$ square cells of unit width) with squares ($1\times1$
tiles) and combs. A $(w_1,g_1,w_2,g_2,\ldots,g_{t-1},w_t)$-comb is composed of
$t$ sub-tiles known as teeth. The $i$-th tooth in the comb has width $w_i$ and
is separated from the $(i+1)$-th tooth by a gap of width $g_i$. Here we only
consider combs with $w_i,g_i\in\mathbb{Z}^+$. When performing a
restricted-overlap tiling of a board with such combs and squares, the leftmost
cell of a tile must be placed in an empty cell whereas the remaining cells in
the tile are permitted to overlap other non-leftmost filled cells of tiles
already on the board.
