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A tournament on 8 or more vertices may be intrinsically linked as a directedgraph. We begin the classification of intrinsically linked tournaments byexamining their score sequences. While many distinct tournaments may have thesame score sequence, there exist score sequences $S$ such that any tournamentwith score sequence $S$ has an embedding with no nonsplit consistently orientedlink. We call such score sequences $\textit{linkless}$, and we show that thevast majority of score sequences for 8 vertex tournaments are linkless.  We also extend these results to $n$ vertex tournaments and are able toclassify many longer score sequences as well. We show that for any $n$, thereexist at least $O(n)$ linkless score sequences, but we conjecture that thefraction of score sequences of length $n$ that are linkless goes to 0 as $n$becomes large.

Classifying Intrinsically Linked Tournaments by Score Sequence