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Enumerating (2+2) -free posets by the number of minimal elements and other statistics

<12>Enumeration of the much-studied (2+2)-free posets, equivalent to the well-known interval orders, was open for 40 years, until a generating function was found in 2010. Our paper provides a substantial generalization of this important generating function, incorporating 4 parameters, including the number of minimal elements, an important poset invariant. The paper has already been influential and led to work by three different researchers (Jelinek, Levande, Yan) who proved a conjecture posed in the paper, substantially simplifying the expression for the generating function and thus making it very useful for further investigation of the several important structures it enumerates.