TY - JOUR
T1 - 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
AU - Langner, Johanna
AU - Witek, Henryk A.
N1 - Publisher Copyright:
© 2022 University of Kragujevac, Faculty of Science. All rights reserved.
PY - 2022
Y1 - 2022
N2 - 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 E◦S(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.
AB - 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 E◦S(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.
UR - http://www.scopus.com/inward/record.url?scp=85129918784&partnerID=8YFLogxK
U2 - 10.46793/match.88-3.747L
DO - 10.46793/match.88-3.747L
M3 - Article
AN - SCOPUS:85129918784
SN - 0340-6253
VL - 88
SP - 747
EP - 765
JO - Match
JF - Match
IS - 3
ER -