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The study of asymptotic minimum degree thresholds that force matchings andtilings in hypergraphs is a lively area of research in combinatorics. A keybreakthrough in this area was a result of H\`{a}n, Person and Schacht whoproved that the asymptotic minimum vertex degree threshold for a perfectmatching in an $n$-vertex $3$-graph is$\left(\frac{5}{9}+o(1)\right)\binom{n}{2}$. In this paper we improve on thisresult, giving a family of degree sequence results, all of which imply theresult of H\`{a}n, Person and Schacht, and additionally allow one third of thevertices to have degree $\frac{1}{9}\binom{n}{2}$ below this threshold.Furthermore, we show that this result is, in some sense, tight.

A degree sequence strengthening of the vertex degree threshold for a perfect matching in 3-uniform hypergraphs