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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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