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<p>We use the Almkvist–Zeilberger algorithm, combined with a weighted version of the Even–Gillis Laguerre integral due to Foata and Zeilberger, in order to efficiently compute weight enumerators of multiset derangements according to the number of cycles. The present paper is inspired by important previous work by Mourad Ismail and his collaborators, done in the late 1970s, but still useful after all these years.</p>

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Efficient weighted counting of multiset derangements

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  • 出版模式：

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  • 发表日期：

    2025年5月18日

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  • Shalosh B. Ekhad,
  • Doron Zeilberger

摘要

We use the Almkvist–Zeilberger algorithm, combined with a weighted version of the Even–Gillis Laguerre integral due to Foata and Zeilberger, in order to efficiently compute weight enumerators of multiset derangements according to the number of cycles. The present paper is inspired by important previous work by Mourad Ismail and his collaborators, done in the late 1970s, but still useful after all these years.