Colored permutations with no monochromatic cycles

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An (n(1), n(2),..., nk)-colored permutation is a permutation of n(1) + n(2) +...+ n(k) in which 1, 2,..., n(1) have color 1, and n(1) + 1, n(1) + 2,..., n(1) + n(2) have color 2, and so on. We give a bijective proof of Steinhardt's result: the number of colored permutations with no monochromatic cycles is equal to the number of permutations with no fixed points after reordering the first n(1) elements, the next n(2) element, and so on, in ascending order. We then find the generating function for colored permutations with no monochromatic cycles. As an application we give a new proof of the well known generating function for colored permutations with no fixed colors, also known as multi-derangements.
Publisher
KOREAN MATHEMATICAL SOC
Issue Date
2017-07
Language
English
Article Type
Article
Keywords

ALTERNATING PERMUTATIONS

Citation

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.54, no.4, pp.1149 - 1161

ISSN
0304-9914
DOI
10.4134/JKMS.j160392
URI
http://hdl.handle.net/10203/225840
Appears in Collection
MA-Journal Papers(저널논문)
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