Hypertournaments-Scores, Losing scores, Total scores and Degrees

Hypertournaments are generalizations of tournaments. We discuss the concept of scores, losing scores, total scores, and degrees in \(k\)-hypertournaments and present characterizations of sequences to be score, losing score, total score, and degree sequences of some \(k\)-hypertournaments. We further discuss stronger upper and lower bounds for scores and losing scores. We extend the concept of scores, losing scores, and degrees to bipartite hypertournaments. In the end, we list some open problems in hypertournaments.