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• W2094047170 abstract "In 1992 Chung, Diaconis and Graham generalized de Bruijn cycles to other combinatorial families with universal cycles . Universal cycles have been investigated for permutations, partitions, k -partitions and k -subsets. In 1990 Hurlbert proved that there exists at least one Ucycle of n − 1 -partitions of an n -set when n is odd and conjectured that when n is even, they do not exist. Herein we prove Hurlbert’s conjecture by establishing algebraic necessary and sufficient conditions for the existence of these Ucycles. We enumerate all such Ucycles for n ≤ 13 and give a lower bound on the total number for all n . Additionally we give ranking and unranking formulae. Finally we discuss the structures of the various solutions." @default.
• W2094047170 created "2016-06-24" @default.
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• W2094047170 date "2009-09-01" @default.
• W2094047170 modified "2023-09-27" @default.
• W2094047170 title "Universal cycles of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si5.gif display=inline overflow=scroll><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-partitions of an <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si6.gif display=inline overflow=scroll><mml:mi>n</mml:mi></mml:math>-set" @default.
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• W2094047170 doi "https://doi.org/10.1016/j.disc.2009.03.002" @default.
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