  Let $S=K[x_1,\dots,x_n]$ be the standard graded polynomial ring, with $K$ a
field, and let ${\bf t}=(t_1,\ldots,t_{d-1})\in{\mathbb{Z}}_{\ge 0}^{d-1}$,
$d\ge 2$, be a $(d-1)$-tuple whose entries are non negative integers. To a
${\bf t}$-spread ideal $I$ in $S$, we associate a unique $f_{\bf t}$-vector and
we prove that if $I$ is ${\bf t}$-spread strongly stable, then there exists a
unique ${\bf t}$-spread lex ideal which shares the same $f_{\bf t}$-vector of
$I$ via the combinatorics of the ${\bf t}$-spread shadows of special sets of
monomials of $S$. Moreover, we characterize the possible $f_{\bf t}$-vectors of
${\bf t}$-vector spread strongly stable ideals generalizing the well-known
theorems of Macaulay and Kruskal-Katona. Finally, we prove that among all ${\bf
t}$-spread strongly stable ideals with the same $f_{\bf t}$-vector, the ${\bf
t}$-spread lex ideals have the largest Betti numbers.
