Abstract
A priority queue can transform a permutation π of a set of size n to some but not necessarily all permutations σ. A recent result of Atkinson and Thiyagarajah [1] states that the number of distinct pairs (π, σ) is (n+1)n−1. Recall that Cayley's Theorem ([2]) states that the number of labelled trees on n+1 nodes is also equal to (n+1)n−1. We present a direct correspondence between these labelled trees and these pairs of permutations and discuss related problems.
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References
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© 1995 Springer-Verlag Berlin Heidelberg
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Golin, M., Zaks, S. (1995). Labelled trees and pairs of input-output permutations in priority queues. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1994. Lecture Notes in Computer Science, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59071-4_55
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DOI: https://doi.org/10.1007/3-540-59071-4_55
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