Dyck paths and a bijection for multisets of hook numbers

Ian Goulden, Alexander Yong
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
We give a bijective proof of a result of Regev and Vershik (Electron J. Combin. 4 (1997) R22) on the equality of two multisets of hook numbers of certain skew-Young diagrams. The bijection is given in terms of Dyck paths, a particular type of lattice path. It is extended to also prove a recent, more reÿned result of Regev (European J. Combin. 21 (2000) 959) , which concerns a special class of skew diagrams.
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