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@article{Blossom2,
    AUTHOR = {Ait-Haddou, R. and Mazure, M.-L.},
     TITLE = {The fundamental blossoming inequality in {C}hebyshev
              spaces---{I}: applications to {S}chur functions},
   JOURNAL = {Found. Comput. Math.},
  FJOURNAL = {Foundations of Computational Mathematics. The Journal of the
              Society for the Foundations of Computational Mathematics},
    VOLUME = {18},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {135--158},
   MRCLASS = {41A50 (65D05 65D17 65D18)},
  MRNUMBER = {3749416},
       Doi = {10.1007/s10208-016-9334-8}}

@article{BGKP-fixeddim,
	Author = {Belton, A. and Guillot, D. and Khare, A. and Putinar,
	M.},
	Date-Added = {2017-05-14 07:07:08 +0000},
	Date-Modified = {2017-05-14 07:09:02 +0000},
	Doi = {10.1016/j.aim.2016.04.016},
	Journal = {Adv. Math.},
	Pages = {325--368},
	Title = {Matrix positivity preservers in fixed dimension. I},
	Volume = {298},
	Year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.aim.2016.04.016}}

@inproceedings{BGKP-FPSAC,
	Author = {Belton, A. and Guillot, D. and Khare, A. and Putinar,
	M.},
	Booktitle = {28th International Conference on Formal Power Series and Algebraic Combinatorics},
	Date-Added = {2017-05-14 07:05:25 +0000},
	Date-Modified = {2017-05-14 07:07:00 +0000},
	Pages = {155--166},
	Publisher = {DMTCS Proceedings},
	Title = {Schur polynomials and matrix positivity preservers},
	Year = {2016}}

@misc{BGKP-hankel,
	Author = {Belton, A. and Guillot, D. and Khare, A. and Putinar,
	M.},
	Date-Added = {2017-05-14 07:09:04 +0000},
	Date-Modified = {2017-05-14 07:09:51 +0000},
	Eprint = {1610.05740},
	Eprinttype = {arxiv},
	Title = {Moment-sequence transforms},
	Year = {2016}}

@article {CGS,
    AUTHOR = {Cuttler, A. and Greene, C. and Skandera, M.},
     TITLE = {Inequalities for symmetric means},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {32},
      YEAR = {2011},
    NUMBER = {6},
     PAGES = {745--761},
   MRCLASS = {05E05},
  MRNUMBER = {2821548},
MRREVIEWER = {Trueman MacHenry},
       Doi = {10.1016/j.ejc.2011.01.020}}

@article {FJS,
    AUTHOR = {Fallat, S. and Johnson, C.R. and Sokal, A.D.},
     TITLE = {Total positivity of sums, {H}adamard products and {H}adamard
              powers: results and counterexamples},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {520},
      YEAR = {2017},
     PAGES = {242--259},
   MRCLASS = {15B48 (15A15 15B05 44A60)},
  MRNUMBER = {3611466},
MRREVIEWER = {Olga Y. Kushel},
       Doi = {10.1016/j.laa.2017.01.013}}

@article{FitzHorn,
	Author = {FitzGerald, C.H. and Horn, R.},
	Date-Added = {2017-05-14 07:15:51 +0000},
	Date-Modified = {2017-05-14 07:17:05 +0000},
	Journal = {J. Math. Anal. Appl.},
	Pages = {633--642},
	Doi = {10.1016/0022-247X(77)90167-6},
	Title = {On fractional Hadamard powers of positive definite matrices},
	Volume = {61},
	Year = {1977}}

@article{horn,
	Author = {Horn, R.},
	Fjournal = {Transactions of the American Mathematical Society},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {60.99 (60.20)},
	Mrnumber = {0264736 (41 \#9327)},
	Mrreviewer = {H. Bergstr{\"o}m},
	Pages = {269--286},
	Doi = {10.1090/S0002-9947-1969-0264736-5},
	Title = {The theory of infinitely divisible matrices and kernels},
	Volume = {136},
	Year = {1969}}

@book {karlin,
    AUTHOR = {Karlin, S.},
     TITLE = {Total positivity. {V}ol. {I}},
 PUBLISHER = {Stanford Univ.~Press, Stanford, Calif.},
      YEAR = {1968},
     PAGES = {576},
   MRCLASS = {46.00 (41.00)},
  MRNUMBER = {0230102},
MRREVIEWER = {I. I. Hirschman, Jr.}}

@misc{KT,
	Author = {Khare, A. and Tao, T.},
	Date-Added = {2018-03-14 07:09:04 +0000},
	Date-Modified = {2018-03-14 07:09:51 +0000},
	Eprint = {1708.05197},
	Eprinttype = {arxiv},
	Title = {On the sign patterns of entrywise positivity preservers
	in fixed dimension},
	Year = {2017}}

@article {LPP,
    AUTHOR = {Lam, T. and Postnikov, A. and Pylyavskyy, P.},
     TITLE = {Schur positivity and {S}chur log concavity},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {129},
      YEAR = {2007},
    NUMBER = {6},
     PAGES = {1611--1622},
   MRCLASS = {05E05},
  MRNUMBER = {2369890},
MRREVIEWER = {Riccardo Biagioli},
       Doi = {10.1353/ajm.2007.0045}}

@book{Macdonald,
    AUTHOR = {Macdonald, I.G.},
     TITLE = {Symmetric functions and {H}all polynomials},
    SERIES = {Oxford Mathematical Monographs},
   EDITION = {Second},
      NOTE = {With contributions by A. Zelevinsky,
              Oxford Science Publications},
 PUBLISHER = {The Clarendon Press, Oxford University Press, New York},
      YEAR = {1995},
     PAGES = {475},
   MRCLASS = {05E05 (05-02 20C30 20C33 20K01 33C80 33D80)},
  MRNUMBER = {1354144 (96h:05207)},
MRREVIEWER = {John R. Stembridge}}

@book {MOA,
    AUTHOR = {Marshall, A.W. and Olkin, I. and Arnold, B.C.},
     TITLE = {Inequalities: theory of majorization and its applications},
    SERIES = {Springer Series in Statistics},
   EDITION = {Second},
 PUBLISHER = {Springer, New York},
      YEAR = {2011},
     PAGES = {909},
   MRCLASS = {26-02 (05-02 26D15 26D20 60E15)},
  MRNUMBER = {2759813}}

@article{Rudin59,
	Author = {Rudin, W.},
	Date-Added = {2012-09-11 11:05:11 -0700},
	Date-Modified = {2012-09-11 11:15:14 -0700},
	Fjournal = {Duke Mathematical Journal},
	Journal = {Duke Math. J.},
	Mrclass = {26.00 (42.00)},
	Mrnumber = {0109204 (22 \#91)},
	Mrreviewer = {S. Bochner},
	Pages = {617--622},
	Doi   = {10.1215/S0012-7094-59-02659-6},
	Title = {Positive definite sequences and absolutely monotonic functions},
	Volume = {26},
        Number = {4},
	Year = {1959}}

@article{Schoenberg42,
	Author = {{S}choenberg, I.J.},
	Date-Added = {2012-09-11 11:05:20 -0700},
	Date-Modified = {2013-11-01 15:12:59 -0700},
	Fjournal = {Duke Mathematical Journal},
	Journal = {Duke Math. J.},
	Mrclass = {42.4X},
	Mrnumber = {0005922 (3,232c)},
	Mrreviewer = {S. Bochner},
	Pages = {96--108},
	Doi   = {10.1215/S0012-7094-42-00908-6},
	Title = {Positive definite functions on spheres},
	Volume = {9},
        Number = {1},
	Year = {1942}}

@article{Schur1911,
	Author = {{S}chur, J.},
	Date-Added = {2012-09-11 11:05:37 -0700},
	Date-Modified = {2012-09-25 11:01:32 -0700},
	Journal = {J. Reine Angew. Math.},
	Pages = {1--28},
	Title = {{B}emerkungen zur {T}heorie der beschr{\"a}nkten {B}ilinearformen mit unendlich vielen {V}er{\"a}nderlichen},
	Volume = {140},
	Year = {1911},
	URL = {https://doi.org/10.1515/crll.1911.140.1}}

@article {Sra,
    AUTHOR = {Sra, S.},
     TITLE = {On inequalities for normalized {S}chur functions},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {51},
      YEAR = {2016},
     PAGES = {492--494},
   MRCLASS = {05E05},
  MRNUMBER = {3398873},
       Doi = {10.1016/j.ejc.2015.07.005}}