

@Misc{4ti2,
  author =   {Ralf Hemmecke and Raymond Hemmecke and Matthias K\"oppe and Peter Malkin and Matthias Walter},
  title =    {4ti2---A software package for algebraic, geometric and 
              combinatorial problems on linear spaces},
  howpublished = {{A}vailable at \url{http://www.4ti2.de}}
}

@article{koeppe:irrational-barvinok,
	Author = {Matthias K{\"o}ppe},
	Doi = {10.1137/060664768},
	Eprint = {math.CO/0603308},
	Journal = {SIAM Journal on Discrete Mathematics},
	Number = 1,
	Pages = {220--236},
	Title = {A primal {B}arvinok algorithm based on irrational decompositions},
	Volume = 21,
	Year = 2007,
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/060664768}}
	

@article{latte1,
title = "Effective lattice point counting in rational convex polytopes",
journal = "Journal of Symbolic Computation",
volume = "38",
number = "4",
pages = "1273 - 1302",
year = "2004",
note = "Symbolic Computation in Algebra and Geometry",
issn = "0747-7171",
doi = "DOI: 10.1016/j.jsc.2003.04.003",
url = "http://www.sciencedirect.com/science/article/pii/S0747717104000422",
author = "De Loera, Jes\'us A. and Raymond Hemmecke and Jeremiah Tauzer and Ruriko Yoshida",
}

@article{howToIntegratePolynomialSimplex,
	Author = {Velleda Baldoni and Nicole Berline and De Loera, Jes{\'u}s A. and Matthias K{\"o}ppe and Mich{\`e}le Vergne},
	Doi = "10.1090/S0025-5718-2010-02378-6",
	Journal = {Mathematics of Computation},
	Number = 273,
	Pages = {297--325},
	Title = {How to Integrate a Polynomial over a Simplex},
	Volume = 80,
	Year = 2011,
	Bdsk-Url-1 = {http://dx.doi.org/10.1090/S0025-5718-2010-02378-6}
}

@Article{latte-integrale-paper,
	Author = {De Loera, Jes\'us A. and Brandon Dutra and Matthias K\"oppe and Stanislav Moreinis and Gregory Pinto and Jianqiu Wu},
	was-eprint = {arXiv:{\penalty0}1108.0117 [math.MG]},
	title = "Software for exact integration of polynomials over polyhedra",
	journal = "Computational Geometry: Theory and Applications",
	volume = 46,
	number = 3,
	pages = "232--252",
	year = 2013,
	issn = "0925-7721",
	doi = "10.1016/j.comgeo.2012.09.001",
	keywords = "Exact integration",
	keywords = "Volume computation",
	keywords = "Integration of polynomials",
	keywords = "Valuations",
	keywords = "Polyhedral computation"
}


@incollection{BarviPom,
	Address = {Cambridge},
	Annote = {identical to barvinok:99},
	Author = {Barvinok, Alexander I. and Pommersheim, James E.},
	Booktitle = {New Perspectives in Algebraic Combinatorics},
	Editor = {Billera, Louis J. and Bj\"orner, Anders and Greene, Curtis and Simion, Rodica E. and Stanley, Richard P.},
	Pages = {91-147},
	Publisher = {Cambridge Univ. Press},
	Series = {Math. Sci. Res. Inst. Publ.},
	Title = {An algorithmic theory of lattice points in polyhedra},
	Volume = 38,
	Year = 1999}
	
	
@incollection {cuww,
   author = {Cornuejols, G. and Urbaniak, R. and Weismantel, R. and Wolsey, L.},
   affiliation = {CMU USA USA},
   title = {Decomposition of integer programs and of generating sets},
   booktitle = {Algorithms — ESA '97},
   series = {Lecture Notes in Computer Science},
   editor = {Burkard, Rainer and Woeginger, Gerhard},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {},
   pages = {92-103},
   volume = {1284},
   url = {http://dx.doi.org/10.1007/3-540-63397-9\_8},
   note = {10.1007/3-540-63397-9\_8},
   year = {1997}
}	






@article{latte2,
title = "Short rational functions for toric algebra and applications",
journal = "Journal of Symbolic Computation",
volume = "38",
number = "2",
pages = "959 - 973",
year = "2004",
note = "",
issn = "0747-7171",
doi = "DOI: 10.1016/j.jsc.2004.02.001",
url = "http://www.sciencedirect.com/science/article/pii/S0747717104000252",
author = "De Loera, J. A. and D. Haws and R. Hemmecke and P. Huggins and B. Sturmfels and R. Yoshida",
}



@incollection {latte3,
   author = {De Loera, J. A. and Haws, D. and Hemmecke, R. and Huggins, P. and Yoshida, R.},
   affiliation = {Dept. of Mathematics, University of California, Davis, CA 95616, USA},
   title = {Three Kinds of Integer Programming Algorithms Based on Barvinok’s Rational Functions},
   booktitle = {Integer Programming and Combinatorial Optimization},
   series = {Lecture Notes in Computer Science},
   editor = {Bienstock, Daniel and Nemhauser, George},
   publisher = {Springer Berlin / Heidelberg},
   isbn = {},
   pages = {3-9},
   volume = {3064},
   url = {http://dx.doi.org/10.1007/978-3-540-25960-2\_19},
   note = {10.1007/978-3-540-25960-2\_19},
   year = {2004}
}


@misc{fukuda,
	Author = {Fukuda, Komei},
	Howpublished = {Available from URL \url{http://www.cs.mcgill.ca/~fukuda/soft/cdd\_home/cdd.html}},
	Title = {{\texttt{cddlib}}, version 094a},
	Year = 2005}


@misc{shoup,
	Author = {Victor Shoup},
	Howpublished = {Available from URL \url{http://www.shoup.net/ntl/}},
	Title = {{NTL}, A Library for doing Number Theory},
	Year = 2005
}

@book{sturmfels,
    AUTHOR = {Sturmfels, B.},
     TITLE = {Gr\"obner bases and convex polytopes},
    SERIES = {University Lecture Series},
    VOLUME = {8},
 PUBLISHER = {American Mathematical Society},
     PLACE = {Providence, RI},
      YEAR = {1996},
     PAGES = {xii+162},
      ISBN = {0-8218-0487-1},
    REVIEW = {\MR{1363949 (97b:13034)}},
}


@book{stanley,
	Author = {Stanley, Richard P.},
	Publisher = {Cambridge},
	Title = {Enumerative Combinatorics},
	Volume = {I},
	Year = 1997}

@article{so-called-paper-1,
	Abstract = {This article concerns the computational problem of counting the lattice
	points inside convex polytopes, when each point must be counted with
	a weight associated to it. We describe an efficient algorithm for
	computing the highest degree coefficients of the weighted Ehrhart
	quasi-polynomial for a rational simple polytope in varying dimension,
	when the weights of the lattice points are given by a polynomial
	function h . Our technique is based on a refinement of an algorithm
	of A. Barvinok in the unweighted case (i.e., h ≡1). In contrast to
	Barvinok's method, our method is local, obtains an approximation
	on the level of generating functions, handles the general weighted
	case, and provides the coefficients in closed form as step polynomials
	of the dilation. To demonstrate the practicality of our approach,
	we report on computational experiments which show that even our simple
	implementation can compete with state-of-the-art software.},
	Affiliation = {Dipartimento di Matematica, Universit{\`a} degli studi di Roma ``Tor Vergata'', Via della ricerca scientifica 1, 00133 Roma, Italy},
	Annote = {This is paper 1. eprint arXiv:{\penalty0}1011.1602 [math.CO]},
	Author = {Velleda Baldoni and Nicole Berline and De Loera, Jes{\'u}s A. and Matthias K{\"o}ppe and Mich{\`e}le Vergne},
	Doi = {10.1007/s10208-011-9106-4},
	Issn = {1615-3375},
	Issue = {4},
	Journal = {Foundations of Computational Mathematics},
	Keyword = {Mathematics and Statistics},
	Pages = {435--469},
	Publisher = {Springer New York},
	Title = {Computation of the Highest Coefficients of Weighted {E}hrhart Quasi-polynomials of Rational Polyhedra},
	Volume = {12},
	Year = {2012},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10208-011-9106-4}}


@book{deloera-hemmecke-koeppe:book,
	Address = {Philadelphia, PA},
	Author = {De Loera, Jes{\'u}s A. and Hemmecke, Raymond and K{\"o}ppe, Matthias},
	Doi = {10.1137/1.9781611972443},
	Isbn = {978-1-61197-243-6},
	Owner = {mkoeppe},
	Pages = {xx+322},
	Publisher = {Society for Industrial and Applied Mathematics},
	Series = {MOS--SIAM Series on Optimization},
	Timestamp = {2012.12.20},
	Title = {Algebraic and Geometric Ideas in the Theory of Discrete Optimization},
	Year = 2013,
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/1.9781611972443}}

@InProceedings{baldoni-et-al:denumerant-fpsac,
  author = 	 {Velleda Baldoni and Nicole Berline and De Loera,
		  Jes{\'u}s A. and Brandon E. Dutra and
                  Matthias K{\"o}ppe and Mich{\`e}le Vergne},
  title = 	 {Top degree coefficients of the Denumerant},
  booktitle = {25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
  year = 	 2013,
  series = 	 {DMTCS proc. AS},
  pages = 	 {1149--1160},
  organization = {Discrete Mathematics and Theoretical Computer Science (DMTCS)},
  annote = 	 {Note that in the journal metadata for this article,
                  De Loera is missing on the author list!  And also
                  the metadata title is different: "Top Coefficients
                  of the Denumerant"},
  issn = {1365--8050},
  url = {http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAS0197/4324}
}

@Misc{baldoni-et-al:denumerant-full-paper,
  author = {Velleda Baldoni and Nicole Berline and  De
                  Loera, Jes{\'u}s A. and Brandon E. Dutra and Matthias K{\"o}ppe and Mich{\`e}le Vergne},
  title =   {Coefficients of {S}ylvester's Denumerant},
  howpublished = {eprint arXiv:{\penalty0}1312.7147 [math.CO]},
  year = {2013},
}

@article{barvinok-2006-ehrhart-quasipolynomial,
	Author = {Barvinok, Alexander I.},
	Equivalent-Entries = {newbar,barvinok-2006-ehrhart-quasipolynomial,Barvinok2006simplex},
	Fjournal = {Mathematics of Computation},
	Journal = {Math. Comp.},
	Number = {255},
	Owner = {mkoeppe},
	Pages = {1449--1466},
	Timestamp = {2012.12.20},
	Title = {Computing the {E}hrhart quasi-polynomial of a rational simplex},
	Volume = {75},
	Year = {2006}}

