On scores in multipartite hypertournaments

In this paper, we discuss two types of hypertournaments, one $[\alpha_i]_1^k$-multipartite hypertournament ($[\alpha_i]_1^k$-MHT) and the second $(\alpha_i)_1^k$-multipartite hypertournament ($(\alpha_i)_1^k$-MHT). We obtain necessary and sufficient conditions for the $k$ lists of non-negative integers in non-decreasing order to be the losing score lists (score lists) of $[\alpha_i]_1^k$-MHT and that of $(\alpha_i)_1^k$-MHT. We extend this concept to more general class of $[\alpha_i]_1^k$-multipartite multihypertournament ($[\alpha_i]_1^k$-MMHT) and $(\alpha_i)_1^k$-multipartite multihypertournament ($(\alpha_i)_1^k$-MMHT).