@article{BereleRegev1987,
  author = {Berele, A. and Regev, A.},
  title = {Hook {Young} diagrams with applications to combinatorics and to representations of {Lie} superalgebras},
  journal = {Advances in Mathematics},
  volume = {64},
  number = {2},
  pages = {118--175},
  year = {1987},
  doi = {10.1016/0001-8708(87)90007-7}
}

@article{DiaconisShahshahani1981,
  author = {Diaconis, Persi and Shahshahani, Mehrdad},
  title = {Generating a random permutation with random transpositions},
  journal = {Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und verwandte Gebiete},
  volume = {57},
  pages = {159--179},
  year = {1981},
  doi = {10.1007/BF00535487}
}

@book{James1978,
  author = {James, Gordon D.},
  title = {The Representation Theory of the Symmetric Groups},
  series = {Lecture Notes in Mathematics},
  volume = {682},
  publisher = {Springer-Verlag},
  year = {1978},
  url = {https://www-users.cse.umn.edu/~webb/oldteaching/Year2010-11/the-representation-theory-of-the-symmetric-groups-SLN.pdf}
}

@book{Sagan2001,author={Sagan, Bruce E.},title={The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions},edition={2},series={Graduate Texts in Mathematics},volume={203},publisher={Springer},year={2001},doi={10.1007/978-1-4757-6804-6}}

@article{Samorodnitsky2008,
  author = {Samorodnitsky, Alex},
  title = {An upper bound for permanents of nonnegative matrices},
  journal = {Journal of Combinatorial Theory, Series A},
  volume = {115},
  number = {2},
  pages = {279--292},
  year = {2008},
  doi = {10.1016/j.jcta.2007.05.010},
  eprint = {math/0605147v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0605147v2},
  note = {arXiv version 2, 23 July 2006}
}

@book{Stanley1999,author={Stanley, Richard P.},title={Enumerative Combinatorics, Volume 2},publisher={Cambridge University Press},year={1999}}

@article{araki1990,
 author={Araki, Huzihiro}, title={On an inequality of {Lieb} and {Thirring}},
 journal={Letters in Mathematical Physics}, volume={19},
 pages={167--170}, year={1990}, doi={10.1007/BF01045887}}

@article{cll2006,
  author = {Carlen, Eric A. and Lieb, Elliott H. and Loss, Michael},
  title = {An inequality of {Hadamard} type for permanents},
  journal = {Methods and Applications of Analysis},
  volume = {13},
  number = {1},
  pages = {1--18},
  year = {2006},
  eprint = {math/0508096v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0508096v1},
  note = {arXiv version 1, 4 August 2005}
}

@article{liebeck-shalev2004,
  author = {Liebeck, Martin W. and Shalev, Aner},
  title = {Fuchsian groups, coverings of {Riemann} surfaces, subgroup growth, random quotients and random walks},
  journal = {Journal of Algebra},
  volume = {276},
  number = {2},
  pages = {552--601},
  year = {2004},
  url = {https://www.ma.imperial.ac.uk/~mwl/fuchs.pdf}
}

@article{mason-niese2016,
  author = {Mason, Sarah K. and Niese, Elizabeth},
  title = {Quasisymmetric $(k,l)$-hook {Schur} functions},
  journal = {Annals of Combinatorics},
  volume = {22},
  pages = {167--199},
  year = {2018},
  doi = {10.1007/s00026-018-0376-2},
  eprint = {1606.06942v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1606.06942v1},
  note = {Author version: arXiv:1606.06942v1, 22 June 2016}
}

@misc{orellana-zabrocki2000,
  author = {Orellana, Rosa C. and Zabrocki, Mike},
  title = {Some remarks on the characters of the general {Lie} superalgebra},
  year = {2000},
  eprint = {math/0008152v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0008152v1},
  note = {Version 1, 18 August 2000}
}


@article{Thorp1973,
 author={Thorp, Edward O.},
 title={Nonrandom shuffling with applications to the game of {Faro}},
 journal={Journal of the American Statistical Association},
 volume={68}, number={344}, pages={842--847}, year={1973},
 doi={10.1080/01621459.1973.10481434}}

@article{Morris2008,
 author={Morris, Ben}, title={The mixing time of the {Thorp} shuffle},
 journal={SIAM Journal on Computing}, volume={38}, number={2},
 pages={484--504}, year={2008}, doi={10.1137/050636231},
 url={https://arxiv.org/abs/math/0507307v1},
 note={Author version: arXiv:math/0507307v1, 15 July 2005}}

@article{MontenegroTetali2006,
 author={Montenegro, Ravi and Tetali, Prasad},
 title={Mathematical aspects of mixing times in {Markov} chains},
 journal={Foundations and Trends in Theoretical Computer Science},
 volume={1}, number={3}, pages={237--354}, year={2006},
 doi={10.1561/0400000003},
 url={https://www.stat.berkeley.edu/~aldous/260-FMIE/Papers/montenegro_tetali.pdf}}

@article{Morris2009,
 author={Morris, Ben},
 title={Improved mixing time bounds for the {Thorp} shuffle and {$L$}-reversal chain},
 journal={Annals of Probability}, volume={37}, number={2},
 pages={453--477}, year={2009}, doi={10.1214/08-AOP409},
 url={https://arxiv.org/abs/0802.0339v1},
 note={Author version: arXiv:0802.0339v1, 4 February 2008}}

@article{Morris2013,
 author={Morris, Ben}, title={Improved mixing time bounds for the {Thorp} shuffle},
 journal={Combinatorics, Probability and Computing}, volume={22},
 number={1}, pages={118--132}, year={2013}, doi={10.1017/S0963548312000478},
 url={https://arxiv.org/abs/0912.2759v1},
 note={Author version: arXiv:0912.2759v1, 14 December 2009}}

@article{audenaert2007,
  author={Audenaert, Koenraad M. R.},
  title={On the {Araki--Lieb--Thirring} inequality},
  journal={International Journal of Information and Systems Sciences},
  volume={4}, number={1}, pages={78--83}, year={2008},
  eprint={math/0701129v2},
  archivePrefix={arXiv},
  url={https://arxiv.org/abs/math/0701129v2},
  note={Author version: arXiv:math/0701129v2, 29 March 2007; Theorem 1}}

@article{BristielCaputo2024,
  author = {Bristiel, Alexandre and Caputo, Pietro},
  title = {Entropy inequalities for random walks and permutations},
  journal = {Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  volume = {60},
  number = {1},
  pages = {54--81},
  year = {2024},
  doi = {10.1214/22-AIHP1267},
  eprint = {2109.06009v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2109.06009v3},
  note = {Author version: arXiv:2109.06009v3, 10 May 2022; Corollary 1.14 and Section 4.3}
}
