Since Cho and Kim (2005) showed that the competition graph of a doubly partial order is an interval graph, it has been actively studied whether or not the same phenomenon occurs for other variants of competition graph and interesting results have bee
n obtained. Continuing in the same spirit, we study the competition hypergraph, an interesting variant of the competition graph, of a doubly partial order. Though it turns out that the competition hypergraph of a doubly partial order is not always interval, we completely characterize the competition hypergraphs of doubly partial orders which are interval.
