Generation of All Possible Multiselections from a Multiset

Thomas Wieder


The concept of a [k1, k2,..., kK]-selection applied on a multiset is introduced and an algorithm is outlined to generate all [k1, k2,..., kK]-selections from a given multiset.

Key words: Multiselection; Mutiset; Contingency matrix; Combinatories


Multiselection; Mutiset; Contingency matrix; Combinatories

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Multiselection.mpl can be found at The corresponding Maple 13 worksheet is available at

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The formula is attributed to Percy Alexander MacMahon, but I failed to find it in his Combinatory Analysis and in his Collected Papers.

A Maple program which implements the formula (5) can be found at http://thomas-wieder.privat.t­

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Unpublished, the Corresponding Maple 13 Worksheet Including Source Code is Available at http://



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