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- W2772961567 abstract "A universal cycle for permutations of length $n$ is a cyclic word, or permutation, whose any factor is order-isomorphic to exactly one permutation of length $n$, and all permutations of length $n$ are contained as a factor. It is well known that universal cycles for permutations of length $n$ exist. However, all known ways to construct such cycles are rather complicated. For example, in the original paper establishing the existence of the universal cycles, constructing such a cycle involves finding an Eulerian cycle in a certain graph and then dealing with partially ordered sets. In this paper, we offer a simple way to generate a universal cycle for permutations of length $n$, which is based on applying a greedy algorithm to a permutation of length $n-1$. We prove that this approach gives a unique universal cycle $Pi_n$ for permutations, and we study properties of $Pi_n$." @default.
- W2772961567 created "2017-12-22" @default.
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- W2772961567 date "2017-11-29" @default.
- W2772961567 modified "2023-09-27" @default.
- W2772961567 title "On a Greedy Algorithm to Construct Universal Cycles for Permutations" @default.
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