2013/09/25 by Andrews, George E., Jelínek, Vít · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1309.6669
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 ∑n≥ 0(1/p;1/q)n= ∑n≥ 0 pqn(p;q)n(q;q)n and ∑n≥ 0 (-1)n(1/p;1/q)n= ∑n≥ 0 pqn(p;q)n(-q;q)n =∑n≥ 0 (q/p)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.