Green matrices associated with generalized linear polyominoes. (English) Zbl 1320.15037
Summary: A polyomino is an edge-connected union of cells in the planar square lattice. Here we consider generalized linear polyominoes; that is, the polyominoes supported by an \(n\times 2\) lattice. In this paper, we obtain the Green function and the Kirchhoff index of a generalized linear polyomino as a perturbation of a \(2n\)-path by adding weighted edges between opposite vertices. This approach deeply links generalized linear polyomino Green functions with the inverse \(M\)-matrix problem, and especially with the so-called Green matrices.
MSC:
| 15B99 | Special matrices |
| 05B50 | Polyominoes |
| 15A09 | Theory of matrix inversion and generalized inverses |
| 39A05 | General theory of difference equations |
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