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

Johanna Langner, Henryk A. Witek

Research output: Contribution to journalArticlepeer-review

Abstract

We report closed-form formulas for the ZZ polynomials of all m-tier regular strips with m = 1 – 6 and an arbitrary length n. The ZZ polynomials were calculated fully automatically using the equivalence between the ZZ polynomial ZZ(S, x) of a regular benzenoid strip S and the extended strict order polynomial ES(n, 1 + x) of the corresponding poset 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.

Original languageEnglish
Pages (from-to)747-765
Number of pages19
JournalMatch
Volume88
Issue number3
DOIs
StatePublished - 2022

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