On the existence of permutations conditioned by certain rational functions

Guo-Niu Han; Guo-Niu Han

doi:10.3934/era.2020009

Electronic Research Archive

2020, Volume 28, Issue 1: 149-156. doi: 10.3934/era.2020009

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On the existence of permutations conditioned by certain rational functions

Guo-Niu Han

I.R.M.A., UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, F-67084 Strasbourg, France

Received: 01 October 2019 Revised: 01 February 2020
05A05, 05B99, 05C05

We prove several conjectures made by Z.-W. Sun on the existence of permutations conditioned by certain rational functions. Furthermore, we fully characterize all integer values of the "inverse difference" rational function. Our proofs consist of both investigation of the mathematical properties of the rational functions and brute-force attack by computer for finding special permutations.
- Permutation,
- rational function,
- existence,
- algorithm,
- binary tree
Citation: Guo-Niu Han. On the existence of permutations conditioned by certain rational functions[J]. Electronic Research Archive, 2020, 28(1): 149-156. doi: 10.3934/era.2020009

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Abstract

We prove several conjectures made by Z.-W. Sun on the existence of permutations conditioned by certain rational functions. Furthermore, we fully characterize all integer values of the "inverse difference" rational function. Our proofs consist of both investigation of the mathematical properties of the rational functions and brute-force attack by computer for finding special permutations.

References

[1]	(2009) Analytic Combinatorics. Cambridge: Cambridge University Press.
[2]	Permutation generation methods. Comput. Surveys (1977) 9: 137-164.
[3]	(2012) Enumerative Combinatorics. Cambridge: Cambridge Studies in Advanced Mathematics, 49, Cambridge University Press.
[4]	Z.-W. Sun, On permutation of $\{1, \ldots, n\}$ and related topics, preprint, arXiv: 1811.10503.

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