Extremal Betti numbers of certain two-dimensional monomial ideals

In this paper, we shall provide explicit formulas for the extremal Betti numbers of $R\mathrm{/}I$, where $I$ is the defining ideal of certain weighted hyperplanes in ${\mathbb{P}}^{n-1}$ and $R$ is the polynomial ring in $n$ indeterminates over a field. As a consequence, we completely classify such ideals which are pseudo-Gorenstein as in sense of V. Ene, J. Herzog, T. Hibi and S. S. Madani.