A property of dominance of partitions
classification
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keywords
dominatesintegerdenotedominancegivenlengthnon-increasingobtained
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Given an integer partition $\la=(\la_1, ..., \la_\ell)$ and an integer k, denote by $\la^{(k)}$ the sequence of length $\ell$ obtained by reordering the values $|\la_i-k|$ in non-increasing order. If $\la$ dominates $\mu$ and has the same weight, then $\la^{(k)}$ dominates $\mu^{(k)}$.
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