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{\bf Lun Lv and Sabrina X. M. Pang}
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{\bf Reduced Decompositions of Matchings}
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We give a characterization of matchings in terms of the canonical
reduced decompositions. As an application, the canonical reduced
decompositions of $12312$-avoiding matchings are obtained. Based on
such decompositions, we find a bijection between $12312$-avoiding
matchings and ternary paths.



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