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@book {Aigner_18,
    AUTHOR = {Aigner,~M. and Ziegler,~G.~M.},
     TITLE = {Proofs from {T}he {B}ook},
   EDITION = {6th~ed.},
 PUBLISHER = {Springer, Berlin},
      YEAR = {2018},
}

@article{Brenti_95,
	AUTHOR = {Brenti,~F.},
	TITLE = {Combinatorics and total positivity},
	JOURNAL = {J.~Combin.~Theory A},
	VOLUME =  {71}, 
	PAGES = {175--218},
	YEAR = {1995}
}

@misc{Sokal_20,
	AUTHOR = {Sokal, A.~D. and Zeng, J.},
	EPRINT = {2003.08192},
	EPRINTTYPE = {arXiv},
	TITLE = {Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions},
	YEAR = {2020}
}

@incollection{Brenti_96,
	AUTHOR = {Brenti,~F.},
	TITLE = {The applications of total positivity
   to combinatorics, and conversely.},
   	YEAR = {1996},
   	BOOKTITLE = {Total Positivity and its Applications},
   	EDITOR = {Gasca, M. and Micchelli, C.~A.},
   	PUBLISHER = {Kluwer},
    ADDRESS = {Dordrecht},
    PAGES = {451--473}
}


@book{Comtet_74,
	AUTHOR = {L.~Comtet}, 
	TITLE = {Advanced Combinatorics: The Art of Finite and Infinite Expansions},
	PUBLISHER = {Reidel},
	ADDRESS = {Dordrecht--Boston},
	YEAR = {1974},
	NOTE = {Translated from the French by J.W.~Nienhuys.
    [French original:  {\em Analyse Combinatoire}\/, tomes~I et II,
    Presses Universitaires de France, Paris, 1970.]}
}

@book{Fallat_11,
	TITLE = {Totally Nonnegative Matrices},
	AUTHOR = {Fallat, S.~M. and Johnson, C.~R.},
	YEAR = {2011},
	PUBLISHER = {Princeton University Press},
	ADDRESS = {Princeton NJ}
}

@article{Fomin_00,
	TITLE = {Total positivity: tests and parametrizations},
	AUTHOR = {Fomin, S. and Zelevinsky, A.},
	JOURNAL = {Math.~Intelligencer},
	VOLUME = {22, no.~1},
	PAGES = {23--33},
	YEAR = {2000}
}

@book{Gantmacher_02,
	TITLE = {Oscillation Matrices and Kernels and Small Vibrations of
       Mechanical Systems},
    AUTHOR = {Gantmacher, F.~R. and Krein, M.~G.},
    YEAR = {2002},
    PUBLISHER = {AMS Chelsea Publishing},
    ADDRESS = {Providence RI},
    NOTE = {Based on the second Russian edition, 1950}
}

@book{Graham_94,
	AUTHOR = {Graham, R.~L. and Knuth, D.~E. and Patashnik, O.},
    TITLE = {Concrete Mathematics: A Foundation for Computer Science},
    EDITION = {2nd ed.},
    PUBLISHER = {Addison-Wesley},
    ADDRESS = {Reading MA},
    YEAR = {1994}
}

@book{Karlin_68,
	AUTHOR = {S.~Karlin},
	TITLE = {Total Positivity},
	PUBLISHER = {Stanford University Press},
	ADDRESS = {Stanford CA}, 
	YEAR = {1968}
}

@online{OEIS,
	TITLE = {The On-Line Encyclopedia of Integer Sequences},
	URL = {https://oeis.org}}

@article{MR4,
AUTHOR = {Corliss, J. J.},
     TITLE = {Upper limits to the real roots of a real algebraic equation},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {46},
      YEAR = {1939},
     PAGES = {334--338},
   MRCLASS = {09.0X},
  MRNUMBER = {0000004},
MRREVIEWER = {O. Sz\'asz},
       DOI = {10.2307/2302887}}

@book{Pinkus_10,
	AUTHOR = {A.~Pinkus},
	TITLE = {Totally Positive Matrices},
    PUBLISHER = {Cambridge University Press},
    ADDRESS = {Cambridge}, 
    YEAR = {2010}
}



@book{Stanley_86,
	AUTHOR = {Stanley, R.~P.},
	TITLE = {Enumerative Combinatorics},
	VOLUME = {1},
	PUBLISHER = {Wadsworth \& Brooks/Cole},
    ADDRESS = {Monterey CA},
    YEAR = {1986},
    NOTE = {Reprinted by Cambridge University Press, 1999}
}