ZZ Polynomials of Regular \(m\)-tier Benzenoid Strips as Extended Strict Order Polynomials of Associated Posets Part 3. Compilation of Results for \(m = 1 - 6\)
Abstract
We report closed-form formulas for the ZZ polynomials of all \(m\)-tier regular strips with \(m=1\,\text{--}\,6\) and an arbitrary length \(n\). The ZZ polynomials were calculated fully automatically using the equivalence between the ZZ polynomial \(\text{ZZ}(\boldsymbol{S},x)\)
of a regular benzenoid strip \(\boldsymbol{S}\) and the extended strict order polynomial \(\text{E}_{\mathcal{S}}^{\circ}(n,1+x)\) of the corresponding poset \(\mathcal{S}\), demonstrated formally in Part 1 of this series and the corresponding
algorithm introduced in Part 2. The results for \(m=1\,-\,5\) reproduce the previous, laboriously-derived collection of formulas, while the results for \(m=6\), constituting about 70% of the presented compilation, are new. The applied
algorithm can be employed just as well for larger regular strips; the scope of the present tabulation is limited by the sheer amount of conceivable regular strips with 7 and more tiers.
