\begin{thebibliography}{AAMP12}

\bibitem[AAMP12]{AritaAyyerMallickProlhac12}
Chikashi Arita, Arvind Ayyer, Kirone Mallick, and Sylvain Prolhac.
\newblock Generalized matrix ansatz in the multispecies exclusion process---the
  partially asymmetric case.
\newblock {\em J. Phys. A}, 45(19):195001, 16, 2012.

\bibitem[AGS18]{AasGrinbergS}
Erik Aas, Darij Grinberg, and Travis Scrimshaw.
\newblock Multiline queues with spectral parameters.
\newblock 2018.
\newblock arXiv:1810.08157.

\bibitem[Ale16]{A}
Per Alexandersson.
\newblock Non-symmetric {M}acdonald polynomials and {D}emazure-{L}usztig
  operators.
\newblock arXiv:1602.05153, 2016.

\bibitem[CdGW]{CGW-arxiv}
Luigi Cantini, Jan de~Gier, and Michael Wheeler.
\newblock Matrix product and sum rule for {M}acdonald polynomials.
\newblock FPSAC abstract.

\bibitem[CdGW15]{CGW}
Luigi Cantini, Jan de~Gier, and Michael Wheeler.
\newblock Matrix product formula for {M}acdonald polynomials.
\newblock {\em J. Phys. A}, 48(38):384001, 25, 2015.

\bibitem[Che91]{Cherednik1}
Ivan Cherednik.
\newblock A unification of {K}nizhnik-{Z}amolodchikov and {D}unkl operators via
  affine {H}ecke algebras.
\newblock {\em Invent. Math.}, 106(2):411--431, 1991.

\bibitem[Che94]{Cherednik2}
Ivan Cherednik.
\newblock Integration of quantum many-body problems by affine
  {K}nizhnik-{Z}amolodchikov equations.
\newblock {\em Adv. Math.}, 106(1):65--95, 1994.

\bibitem[Che95]{Cher1}
Ivan Cherednik.
\newblock Nonsymmetric {M}acdonald polynomials.
\newblock {\em Internat. Math. Res. Notices}, (10):483--515, 1995.

\bibitem[DEHP93]{DEHP}
B.~Derrida, M.~R. Evans, V.~Hakim, and V.~Pasquier.
\newblock Exact solution of a {$1$}{D} asymmetric exclusion model using a
  matrix formulation.
\newblock {\em J. Phys. A}, 26(7):1493--1517, 1993.

\bibitem[EFM09]{EvansFerrariMallick08}
Martin~R. Evans, Pablo~A. Ferrari, and Kirone Mallick.
\newblock Matrix representation of the stationary measure for the multispecies
  {TASEP}.
\newblock {\em J. Stat. Phys.}, 135(2):217--239, 2009.

\bibitem[Fer11]{thesis}
Jeffrey~Paul Ferreira.
\newblock Row-strict quasisymmetric schur functions, characterizations of
  demazure atoms, and permuted basement nonsymmetric {M}acdonald polynomials.
\newblock 2011.

\bibitem[FM07]{FerrariMartin}
Pablo~A. Ferrari and James~B. Martin.
\newblock Stationary distributions of multi-type totally asymmetric exclusion
  processes.
\newblock {\em Ann. Probab.}, 35(3):807--832, 2007.

\bibitem[Hai01]{HaimanHilbert}
Mark Haiman.
\newblock Hilbert schemes, polygraphs and the {M}acdonald positivity
  conjecture.
\newblock {\em J. Amer. Math. Soc.}, 14(4):941--1006, 2001.

\bibitem[Hai06]{HaimanICM}
Mark Haiman.
\newblock Cherednik algebras, {M}acdonald polynomials and combinatorics.
\newblock In {\em International {C}ongress of {M}athematicians. {V}ol. {III}},
  pages 843--872. Eur. Math. Soc., Z\"urich, 2006.

\bibitem[HHL05a]{HHL1}
J.~Haglund, M.~Haiman, and N.~Loehr.
\newblock A combinatorial formula for {M}acdonald polynomials.
\newblock {\em J. Amer. Math. Soc.}, 18(3):735--761, 2005.

\bibitem[HHL05b]{HHL2}
J.~Haglund, M.~Haiman, and N.~Loehr.
\newblock Combinatorial theory of {M}acdonald polynomials. {I}. {P}roof of
  {H}aglund's formula.
\newblock {\em Proc. Natl. Acad. Sci. USA}, 102(8):2690--2696, 2005.

\bibitem[HHL08]{HHL3}
J.~Haglund, M.~Haiman, and N.~Loehr.
\newblock A combinatorial formula for nonsymmetric {M}acdonald polynomials.
\newblock {\em Amer. J. Math.}, 130(2):359--383, 2008.

\bibitem[KT07]{KasataniTakeyama}
Masahiro Kasatani and Yoshihiro Takeyama.
\newblock The quantum {K}nizhnik-{Z}amolodchikov equation and non-symmetric
  {M}acdonald polynomials.
\newblock {\em Funkcial. Ekvac.}, 50(3):491--509, 2007.

\bibitem[Len09]{Lenart}
Cristian Lenart.
\newblock On combinatorial formulas for {M}acdonald polynomials.
\newblock {\em Adv. Math.}, 220(1):324--340, 2009.

\bibitem[Mac95]{Macdonald}
I.~G. Macdonald.
\newblock {\em Symmetric functions and {H}all polynomials}.
\newblock Oxford Mathematical Monographs. The Clarendon Press, Oxford
  University Press, New York, second edition, 1995.
\newblock With contributions by A. Zelevinsky, Oxford Science Publications.

\bibitem[Mac96]{MacdonaldBourbaki}
I.~G. Macdonald.
\newblock Affine {H}ecke algebras and orthogonal polynomials.
\newblock {\em Ast\'erisque}, (237):Exp. No. 797, 4, 189--207, 1996.
\newblock S\'eminaire Bourbaki, Vol. 1994/95.

\bibitem[Mac03]{MacdonaldAffine}
I.~G. Macdonald.
\newblock {\em Affine {H}ecke algebras and orthogonal polynomials}, volume 157
  of {\em Cambridge Tracts in Mathematics}.
\newblock Cambridge University Press, Cambridge, 2003.

\bibitem[Mar99]{Marshall}
Dan Marshall.
\newblock Symmetric and nonsymmetric {M}acdonald polynomials.
\newblock {\em Ann. Comb.}, 3(2-4):385--415, 1999.
\newblock On combinatorics and statistical mechanics.

\bibitem[Mar18]{Martin}
James~B. Martin.
\newblock Stationary distributions of the multi-type {A}{S}{E}{P}s.
\newblock 2018.
\newblock arXiv:1810.10650.

\bibitem[MGP68]{bio}
J~Macdonald, J~Gibbs, and A~Pipkin.
\newblock Kinetics of biopolymerization on nucleic acid templates.
\newblock {\em Biopolymers}, 6, 1968.

\bibitem[PEM09]{ProlhacEvansMallick09}
S.~Prolhac, M.~R. Evans, and K.~Mallick.
\newblock The matrix product solution of the multispecies partially asymmetric
  exclusion process.
\newblock {\em J. Phys. A}, 42(16):165004, 25, 2009.

\bibitem[RY11]{RamYip}
Arun Ram and Martha Yip.
\newblock A combinatorial formula for {M}acdonald polynomials.
\newblock {\em Adv. Math.}, 226(1):309--331, 2011.

\bibitem[Sch06]{Schwer}
Christoph Schwer.
\newblock Galleries, {H}all-{L}ittlewood polynomials, and structure constants
  of the spherical {H}ecke algebra.
\newblock {\em Int. Math. Res. Not.}, pages Art. ID 75395, 31, 2006.

\bibitem[Spi70]{Spitzer}
Frank Spitzer.
\newblock Interaction of {M}arkov processes.
\newblock {\em Advances in Math.}, 5:246--290 (1970), 1970.

\end{thebibliography}