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A derangement is a permutation that has no fixed points. In this paper, we are interested in the proportion of derangements of the finite affine general linear groups. We prove… Click to show full abstract
A derangement is a permutation that has no fixed points. In this paper, we are interested in the proportion of derangements of the finite affine general linear groups. We prove a remarkably simple and explicit formula for this proportion. We also give a formula for the proportion of derangements of prime power order. Both formulae rely on a result of independent interest on partitions: we determine the generating function for the partitions with m parts and with the kth largest part not k, for every $$k\in \mathbb {N}$$k∈N.
Keywords:
derangements prime;
linear groups;
power order;
general linear;
prime power;
affine general
Journal Title: Journal of Algebraic Combinatorics
Year Published: 2017
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Journal Title: Journal of Algebraic Combinatorics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!