On the existence of permutations conditioned by certain rational functions

  • 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.

    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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  • 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.



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    [1] (2009) Analytic Combinatorics.Cambridge University Press.
    [2] Permutation generation methods. Comput. Surveys (1977) 9: 137-164.
    [3] (2012) Enumerative Combinatorics.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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