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@techreport{Diaconis,
	title={Finite Fourier Methods: Access to Tools},
	author={Diaconis, P.},
	year={1990},
	institution={University of Stanford}
}


@phdthesis{Greenhalgh,
	author       = {Greenhalgh, A.}, 
	title        = {Random walks on groups with subgroup invariance properties},
	school       = {University of Stanford},
	year         = 1987,
}


@book{Delsarte,
	title={An Algebraic Approach to the Association Schemes of Coding Theory},
	author={Delsarte, P.},
	series={Philips journal of research / Supplement},
	year={1973},
	publisher={N.V. Philips' Gloeilampenfabrieken}
}


@article{Ambainis,
	author = {Ambainis, A. and Magnin, L. and Roetteler, M. and Roland, J.},
	year = {2010},
	month = {12},
	pages = {},
	title = {Symmetry-Assisted Adversaries for Quantum State Generation},
	journal = {Electronic Colloquium on Computational Complexity - ECCC},
	doi = {10.1109/CCC.2011.24}
}


@article{BR,
	author = {Belovs, A. and Rosmanis, A.},
	title = {Adversary Lower Bounds for the Collision and the Set Equality Problems},
	year = {2018},
	issue_date = {March 2018},
	publisher = {Rinton Press, Incorporated},
	address = {Paramus, NJ},
	volume = {18},
	number = {3–4},
	journal = {Quantum Info. Comput.},
	month = mar,
	pages = {198–222},
	numpages = {25},
	keywords = {quantum query complexity, symmetric group, representation theory}
}




@article{Bogaerts,
	author = {Bogaerts, M.},
	year = {2010},
	month = {10},
	pages = {},
	title = {New Upper Bounds for the Size of Permutation Codes via Linear Programming},
	volume = {17},
	journal = {Electr. J. Comb.},
	doi = {10.37236/407}
}

@article{Chen,
	title = "On the eigenvalues of certain Cayley graphs and arrangement graphs",
	journal = "Linear Algebra and its Applications",
	volume = "444",
	pages = "246 - 253",
	year = "2014",
	doi = "https://doi.org/10.1016/j.laa.2013.11.035",
	author = {Chen, B.F. and Ghorbani, E. and  Wong, K.B.},
	keywords = "Arrangement graph, Cayley graph, Symmetric group, Spectrum integrality",
	abstract = "In this paper, we show that the eigenvalues of certain classes of Cayley graphs are integers. The (n,k,r)-arrangement graph A(n,k,r) is a graph with all the k-permutations of an n-element set as vertices where two k-permutations are adjacent if they differ in exactly r positions. We establish a relation between the eigenvalues of the arrangement graphs and the eigenvalues of certain Cayley graphs. As a result, the conjecture on integrality of eigenvalues of A(n,k,1) follows."
}

@ARTICLE{CKL,  author={{Colbourn}, C. J.  and  {Klove}, T. and  {Ling}, A. C. H.},  journal={IEEE Transactions on Information Theory},   title={Permutation arrays for powerline communication and mutually orthogonal latin squares},   year={2004},  volume={50},  number={6},  pages={1289-1291},}

@article{Dukes,
	author = {Dukes,  P.J.},
	title = {Coding with Injections},
	year = {2012},
	issue_date = {December  2012},
	publisher = {Kluwer Academic Publishers},
	address = {USA},
	volume = {65},
	number = {3},
	doi = {10.1007/s10623-011-9547-4},
	journal = {Des. Codes Cryptography},
	month = dec,
	pages = {213–222},
	numpages = {10},
	keywords = {Ordered design, 94A10, Secondary 05B40, Injection, Permutation code, Primary 05A05, Arrangement, Hamming distance}
}



@article{Huc,
	author = {Huczynska, S.},
	year = {2010},
	month = {02},
	pages = {109-120},
	title = {Equidistant frequency permutation arrays and related constant composition codes},
	volume = {54},
	journal = {Des. Codes Cryptography},
	doi = {10.1007/s10623-009-9312-0}
}

@InProceedings{LR,
	author =	{Lindzey, N. and Rosmanis, A.},
	title =	{{A Tight Lower Bound For Non-Coherent Index Erasure}},
	booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
	pages =	{59:1--59:37},
	series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
	year =	{2020},
	volume =	{151},
	editor =	{Thomas Vidick},
	publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
	address =	{Dagstuhl, Germany},
	optURL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11744},
	URN =		{urn:nbn:de:0030-drops-117446},
	doi =		{10.4230/LIPIcs.ITCS.2020.59},
	annote =	{Keywords: General Adversary Method, Quantum Query Complexity, Association Schemes, Krein Parameters, Representation Theory}
}

@book{MacDonald95,
	author        = {MacDonald, I.G. and Zelevinsky, A.V.},
	title         = "{Symmetric functions and Hall polynomials; 2nd ed.}",
	publisher     = "Oxford University Press",
	address       = "Oxford",
	series        = "Oxford classic texts in the physical sciences",
	year          = "1998",
	url           = "https://cds.cern.ch/record/2019755",
}



@misc{M, 
	AUTHOR = {Munemasa, A.}, 
	TITLE = {The injection scheme of permutations},
	url = "http://math.is.tohoku.ac.jp/~munemasa/documents/2001-KusatsuReport.pdf", 
	YEAR = {2001}}


@misc{Godsil, 
	AUTHOR = {Godsil, C.}, 
	TITLE = {Association Schemes},
	url= {http://www.math.uwaterloo.ca/~cgodsil/pdfs/assoc2.pdf}, 
	YEAR = {2018}}


@article{Strahov,
	title = "Generalized characters of the symmetric group",
	journal = "Advances in Mathematics",
	volume = "212",
	number = "1",
	pages = "109 - 142",
	year = "2007",
	doi = "https://doi.org/10.1016/j.aim.2006.09.017",
	opturl = "http://www.sciencedirect.com/science/article/pii/S0001870806003355",
	author = {Strahov, E.},
	keywords = "Symmetric group, Gelfand pairs, Characters, Symmetric functions",
	abstract = "Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diagS(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand pair (S(n)×S(n−1),diagS(n−1)). Zonal spherical functions of this Gelfand pair form an orthogonal basis in a larger space of functions on S(n), namely in the space of functions invariant with respect to conjugations by S(n−1). We refer to these zonal spherical functions as normalized generalized characters of S(n). The main discovery of the present paper is that these generalized characters can be computed on the same level as the irreducible characters of the symmetric group. The paper gives a Murnaghan–Nakayama type rule, a Frobenius type formula, and an analogue of the determinantal formula for the generalized characters of S(n)."
}

@article{T,
	title = "Upper Bounds on Permutation Codes via Linear Programming",
	journal = "European Journal of Combinatorics",
	volume = "20",
	number = "1",
	pages = "101 - 114",
	year = "1999",
	doi = "https://doi.org/10.1006/eujc.1998.0272",
	opturl = "http://www.sciencedirect.com/science/article/pii/S0195669898902724",
	author = {Tarnanen, H.},
	abstract = "An upper bound on permutation codes of lengthnis given. This bound is a solution of a certain linear programming problem and is based on the well-developed theory of association schemes. Several examples are presented. For instance, the 255 values of the bound forn≤ 8 are tabulated. It turns out that, forn≤ 8, the Kiyota bound for group codes also holds for unrestricted codes at least in 178 cases. Also an easier (but weaker) polynomial version of the bound is given. It is obtained by showing that the mappingsFk(θ) (0≤k≤n/2), whereFkis the Charlier polynomial of degreekand θ the natural character of the symmetric groupSn, are mutually orthogonal characters ofSn."
}