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Omega and related polynomials of polyomino chains of $$4 k$$-cycles. (English) Zbl 07244494
Summary: Omega polynomial of a graph $$G$$ is defined, on the ground of “opposite edge strips” ops: $$\Omega(G;y)=\sum\limits_c m(G,c)x^c$$, where $$m(G,c)$$ is the number of ops strips of length $$c$$. The Sadhana polynomial $$Sd(G;x)$$ can also be calculated by ops counting. In this paper we compute these polynomials for polyomino chains of $$4k$$-cycles. Also by using Omega polynomial we can compute the (edge) PI$$_c$$ polynomial for this graph.
##### MSC:
 12 Field theory and polynomials 05 Combinatorics
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