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Let $M$ be a given real quadratic field. We give a fast algorithm for determining all dihedral quartic fields $K$ with mixed signature having power integral bases and containing $M$ as a subfield. We also determine all generators of power integral bases in $K$. Our algorithm combines a recent result of Kable [9] with the algorithm of Gaál, Pethö and Pohst [6], [7]. To illustrate the method we performed computations for $M=\mathbb{Q}\left(\sqrt{2}\right),\mathbb{Q}\left(\sqrt{3}\right),\mathbb{Q}\left(\sqrt{5}\right).$

We give a graph theoretic interpretation of $r$-Lah numbers, namely, we show that the $r$-Lah number ${⌊\genfrac{}{}{0pt}{}{n}{k}⌋}_r$ counting the number of $r$-partitions of an $(n+r)$-element set into $k+r$ ordered blocks is just equal to the number of matchings consisting of $n-k$ edges in the complete bipartite graph with partite sets of cardinality $n$ and $n+2r-1$ ($0\le k\le n$, $r\ge 1$). We present five independent proofs including a direct, bijective one. Finally, we close our work with a similar result for $r$-Stirling numbers of the second kind.