@article {StemConj,
    AUTHOR = {Stembridge, J. R.},
     TITLE = {Some conjectures for immanants},
   JOURNAL = {Canad. J. Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'{e}matiques},
    VOLUME = {44},
      YEAR = {1992},
    NUMBER = {5},
     PAGES = {1079--1099},
      ISSN = {0008-414X},
       DOI = {10.4153/CJM-1992-066-1},
}

@article {GJ,
	AUTHOR = {Goulden, I. P. and Jackson, D. M.},
	TITLE = {Immanants of combinatorial matrices},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	VOLUME = {148},
	YEAR = {1992},
	NUMBER = {2},
	PAGES = {305--324},
	ISSN = {0021-8693},
	DOI = {10.1016/0021-8693(92)90196-S}
}

@article {Greene,
	AUTHOR = {Greene, Curtis},
	TITLE = {Proof of a conjecture on immanants of the {J}acobi-{T}rudi
	matrix},
	JOURNAL = {Linear Algebra Appl.},
	FJOURNAL = {Linear Algebra and its Applications},
	VOLUME = {171},
	YEAR = {1992},
	PAGES = {65--79},
	ISSN = {0024-3795},
	DOI = {10.1016/0024-3795(92)90250-E},
}
@article {HaiConj,
	AUTHOR = {Haiman, Mark},
	TITLE = {Hecke algebra characters and immanant conjectures},
	JOURNAL = {J. Amer. Math. Soc.},
	FJOURNAL = {Journal of the American Mathematical Society},
	VOLUME = {6},
	YEAR = {1993},
	NUMBER = {3},
	PAGES = {569--595},
	ISSN = {0894-0347},
	DOI = {10.2307/2152777},
}
@article {StemTNN,
	AUTHOR = {Stembridge, John R.},
	TITLE = {Immanants of totally positive matrices are nonnegative},
	JOURNAL = {Bull. London Math. Soc.},
	FJOURNAL = {The Bulletin of the London Mathematical Society},
	VOLUME = {23},
	YEAR = {1991},
	NUMBER = {5},
	PAGES = {422--428},
	ISSN = {0024-6093},
	DOI = {10.1112/blms/23.5.422},
}

@incollection {LusTPGr,
	AUTHOR = {Lusztig, G.},
	TITLE = {Total positivity in reductive groups},
	BOOKTITLE = {Lie theory and geometry},
	SERIES = {Progr. Math.},
	VOLUME = {123},
	PAGES = {531--568},
	PUBLISHER = {Birkh\"{a}user Boston, Boston, MA},
	YEAR = {1994},
	DOI = {10.1007/978-1-4612-0261-5_20},
}
@article {RS,
	AUTHOR = {Rhoades, Brendon and Skandera, Mark},
	TITLE = {Kazhdan-{L}usztig immanants and products of matrix minors},
	JOURNAL = {J. Algebra},
	FJOURNAL = {Journal of Algebra},
	VOLUME = {304},
	YEAR = {2006},
	NUMBER = {2},
	PAGES = {793--811},
	ISSN = {0021-8693},
	DOI = {10.1016/j.jalgebra.2005.07.017},
}

@article {Skan,
	AUTHOR = {Skandera, Mark},
	TITLE = {On the dual canonical and {K}azhdan-{L}usztig bases and 3412-,
	4231-avoiding permutations},
	JOURNAL = {J. Pure Appl. Algebra},
	FJOURNAL = {Journal of Pure and Applied Algebra},
	VOLUME = {212},
	YEAR = {2008},
	NUMBER = {5},
	PAGES = {1086--1104},
	ISSN = {0022-4049},
	MRCLASS = {05E05 (15A15 20C08)},
	MRNUMBER = {2387587},
	MRREVIEWER = {Fabrizio Caselli},
	DOI = {10.1016/j.jpaa.2007.09.007},
}




@book {BB,
	AUTHOR = {Bj\"{o}rner, Anders and Brenti, Francesco},
	TITLE = {Combinatorics of {C}oxeter groups},
	SERIES = {Graduate Texts in Mathematics},
	VOLUME = {231},
	PUBLISHER = {Springer, New York},
	YEAR = {2005},
	PAGES = {xiv+363},
	ISBN = {978-3540-442387; 3-540-44238-3},
	MRCLASS = {05-01 (05E15 20F55)},
	MRNUMBER = {2133266},
	MRREVIEWER = {Jian-yi Shi},
}
@article {Sjo,
	AUTHOR = {Sj\"{o}strand, Jonas},
	TITLE = {Bruhat intervals as rooks on skew {F}errers boards},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {114},
	YEAR = {2007},
	NUMBER = {7},
	PAGES = {1182--1198},
	ISSN = {0097-3165},
	DOI = {10.1016/j.jcta.2007.01.001},
}

@article {FZTNNSemisimple,
	AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
	TITLE = {Totally nonnegative and oscillatory elements in semisimple
	groups},
	JOURNAL = {Proc. Amer. Math. Soc.},
	FJOURNAL = {Proceedings of the American Mathematical Society},
	VOLUME = {128},
	YEAR = {2000},
	NUMBER = {12},
	PAGES = {3749--3759},
	ISSN = {0002-9939},
	DOI = {10.1090/S0002-9939-00-05487-3},
}


@misc{kPosTests,
	title={Parametrizations of $k$-Nonnegative Matrices: Cluster Algebras and $k$-Positivity Tests},
	author={Anna Brosowsky and Sunita Chepuri and Alex Mason},
	year={2017},
	eprint={1712.05037},
	archivePrefix={arXiv},
	primaryClass={math.CO}
}

@misc{Pyl,
	title={personal communication},
	author={Pavlo Pylyavskyy},
}


@article {CA3,
	AUTHOR = {Berenstein, Arkady and Fomin, Sergey and Zelevinsky, Andrei},
	TITLE = {Cluster algebras. {III}. {U}pper bounds and double {B}ruhat
	cells},
	JOURNAL = {Duke Math. J.},
	FJOURNAL = {Duke Mathematical Journal},
	VOLUME = {126},
	YEAR = {2005},
	NUMBER = {1},
	PAGES = {1--52},
	ISSN = {0012-7094},
	DOI = {10.1215/S0012-7094-04-12611-9},
}
@inproceedings {KLPoincare,
	AUTHOR = {Kazhdan, David and Lusztig, George},
	TITLE = {Schubert varieties and {P}oincar\'{e} duality},
	BOOKTITLE = {Geometry of the {L}aplace operator ({P}roc. {S}ympos. {P}ure
	{M}ath., {U}niv. {H}awaii, {H}onolulu, {H}awaii, 1979)},
	SERIES = {Proc. Sympos. Pure Math., XXXVI},
	PAGES = {185--203},
	PUBLISHER = {Amer. Math. Soc., Providence, R.I.},
	YEAR = {1980},
}
@article {LSsmoothSchub,
	AUTHOR = {Lakshmibai, V. and Sandhya, B.},
	TITLE = {Criterion for smoothness of {S}chubert varieties in {${\rm
	Sl}(n)/B$}},
	JOURNAL = {Proc. Indian Acad. Sci. Math. Sci.},
	FJOURNAL = {Indian Academy of Sciences. Proceedings. Mathematical
	Sciences},
	VOLUME = {100},
	YEAR = {1990},
	NUMBER = {1},
	PAGES = {45--52},
	ISSN = {0253-4142},
	DOI = {10.1007/BF02881113},
}
@article {Ten,
	AUTHOR = {Tenner, Bridget Eileen},
	TITLE = {Pattern avoidance and the {B}ruhat order},
	JOURNAL = {J. Combin. Theory Ser. A},
	FJOURNAL = {Journal of Combinatorial Theory. Series A},
	VOLUME = {114},
	YEAR = {2007},
	NUMBER = {5},
	PAGES = {888--905},
	ISSN = {0097-3165},
	DOI = {10.1016/j.jcta.2006.10.003},
}

@misc{oeis, 
    AUTHOR={Vincent Vatter},
    TITLE={Comment on Sequence A052980},
    NOTE={The On-Line Encyclopedia of Integer Sequences},
    URL={http://oeis.org/A052980},
    YEAR={2008},
    MONTH={May},
}

@misc{paper,
    title={1324- and 2143-avoiding Kazhdan--Lusztig imma\-nants and k-positivity},
    author={Sunita Chepuri and Melissa Sherman-Bennett},
    year={2020},
    eprint={2002.07851},
    archivePrefix={arXiv},
}