On q-series identities related to interval orders

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Abstract

We prove several power series identities involving the refined generating function of interval orders, as well as the refined generating function of the self-dual interval orders. These identities may be expressed as n0(1p;1q)n=n0pqn(p;q)n(q;q)n and n0(1)n(1p;1q)n=n0pqn(p;q)n(q;q)n=n0(qp)n(p;q2)n, where the equalities apply to the (purely formal) power series expansions of the above expressions at p=q=1, as well as at other suitable roots of unity.

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