  For positive integers $r$ and $t$, the hypergraph matching Ramsey number
$R_r(s_1,\ldots,s_t)$ is the least integer $n$ such that for any $t$-hyperedge
coloring of complete $r$-uniform hypergraph $K_n^r$, there exists at least one
$j\in\{1,2,\ldots,t\}$ such that the subhypergraph of all hyperedges receiving
color $j$ contains at least one matching of size $s_j$. This parameter was
completely determined by Alon, Frankl, and Lov\'asz in 1986.
  In 2015, the first present author and Hossein Hajiabolhassan found a sharp
lower bound for the chromatic number of general Kneser hypergraphs by means of
the notion of alternation number of hypergraphs. In this paper, as our first
result, we establish a theory to give a development of this result. Doing so,
as our second result, we resolve the problem of characterizing
$R_r(s_1,s_2,\ldots,s_t)$. Our final result is introducing a generalization of
$\mathbf{\mathbb{Z}_p}$-Tucker Lemma together with an application of this
generalized lemma in determining the matching Ramsey number
$R_r(s_1,s_2,\ldots,s_t)$.
