Louis J. Billera

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All published works

Action	Title	Year	Authors
+	Boolean product polynomials and Schur-positivity	2018	Louis J. Billera Sara Billey Vasu Tewari
+	How to decompose a permutation into a pair of labeled Dyck paths by playing a game	2015	Louis J. Billera Lionel Levine Karola Mészáros
+	Bandwidth of the product of paths of the same length	2013	Louis J. Billera Saúl A. Blanco
+	How to decompose a permutation into a pair of labeled Dyck paths by playing a game	2013	Louis J. Billera Lionel Levine Karola Mészáros
+	How to decompose a permutation into a pair of labeled Dyck paths by playing a game	2013	Louis J. Billera Lionel Levine Karola Mészáros
+	Bandwidth of the product of paths of the same length	2012	Louis J. Billera Saúl A. Blanco
+ PDF Chat	Nonpolytopal Nonsimplicial Lattice Spheres with Nonnegative Toric g-Vector	2012	Louis J. Billera Eran Nevo
+	Maximal unbalanced families	2012	Louis J. Billera Justin Tatch Moore C. Dufort Moraites Y. Wang Kenneth S. Williams
+	Bandwidth of the product of paths of the same length	2012	Louis J. Billera Saúl A. Blanco
+	Nonpolytopal nonsimplicial lattice spheres with nonnegative toric g-vector	2011	Louis J. Billera Eran Nevo
+ PDF Chat	Quasisymmetric functions and Kazhdan-Lusztig polynomials	2011	Louis J. Billera Francesco Brenti
+	Flag Enumeration in Polytopes, Eulerian Partially Ordered Sets and Coxeter Groups	2011	Louis J. Billera
+	Nonpolytopal nonsimplicial lattice spheres with nonnegative toric g-vector	2011	Louis J. Billera Eran Nevo
+	A quasisymmetric function for matroids	2009	Louis J. Billera Ning Jia Victor Reiner
+	Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres	2008	Louis J. Billera Samuel K. Hsiao J. Scott Provan
+	The mentor	2008	Louis J. Billera
+	Distance computation in the space of phylogenetic trees	2008	Louis J. Billera Megan Owen
+ PDF Chat	Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres	2007	Louis J. Billera Samuel K. Hsiao J. Scott Provan
+	Quasisymmetric functions and Kazhdan-Lusztig polynomials	2007	Louis J. Billera Francesco Brenti
+	Peak Quasisymmetric Functions and Eulerian Enumeration	2007	Louis J. Billera Samuel K. Hsiao Stephanie van Willigenburg
+	A quasisymmetric function for matroids	2006	Louis J. Billera Ning Jia Victor Reiner
+	Angle sums on polytopes and polytopal complexes	2006	Louis J. Billera Kristin A. Camenga
+	A quasisymmetric function for matroids	2006	Louis J. Billera Ning Jia Victor Reiner
+	Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions	2005	Louis J. Billera Hugh Thomas Stephanie van Willigenburg
+	Enumeration of Flags in Eulerian Posets	2005	Louis J. Billera
+	Enumeration in convex geometries and associated polytopal subdivisions of spheres	2005	Louis J. Billera Samuel K. Hsiao J. Scott Provan
+ PDF Chat	Face Numbers of Polytopes and Complexes	2004	Louis J. Billera Anders Björner
+	Shift techniques and multicover inequalities on colored complexes	2004	Louis J. Billera S. A. Walker
+	Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions	2004	Louis J. Billera Hugh Thomas Stephanie van Willigenburg
+	Peak quasisymmetric functions and Eulerian enumeration	2003	Louis J. Billera Samuel K. Hsiao Stephanie van Willigenburg
+	Erratum to: “Geometry of the Space of Phylogenetic Trees”	2002	Louis J. Billera Susan Holmes Karen Vogtmann
+ PDF Chat	A Geometric Interpretation of the Metropolis-Hastings Algorithm	2001	Louis J. Billera Persi Diaconis
+	Geometry of the Space of Phylogenetic Trees	2001	Louis J. Billera Susan Holmes Karen Vogtmann
+	None	2000	Louis J. Billera Gábor Hetyei
+	Monotonicity of the cd-index for polytopes	2000	Louis J. Billera Richard Ehrenborg
+	Geometry of the space of phylogenetic trees	2000	Louis J. Billera Susan Holmes Karen Vogtmann
+ PDF Chat	None	2000	Louis J. Billera Niandong Liu
+	Linear Inequalities for Flags in Graded Partially Ordered Sets	2000	Louis J. Billera Gábor Hetyei
+	Random Walks and Plane Arrangements in Three Dimensions	1999	Louis J. Billera Kenneth S. Brown Persi Diaconis
+	Random Walks and Plane Arrangements in Three Dimensions	1999	Louis J. Billera Kenneth S. Brown Persi Diaconis
+ PDF Chat	The geometry of products of minors	1998	Eric Babson Louis J. Billera
+	The cd-Index of Zonotopes and Arrangements	1998	Louis J. Billera Richard Ehrenborg Margaret Readdy
+	None	1998	Louis J. Billera Amy N. Myers
+	Neighborly cubical spheres and a cubical lower bound conjecture	1997	Eric Babson Louis J. Billera Clara S. Chan
+	Thec-2d-Index of Oriented Matroids	1997	Louis J. Billera Richard Ehrenborg Margaret Readdy
+	Linear inequalities for flags in graded posets	1997	Louis J. Billera Gábor Hetyei
+	Book reviews	1996	Louis J. Billera
+ PDF Chat	All 0–1 polytopes are traveling salesman polytopes	1996	Louis J. Billera A. Sarangarajan
+	Formal power series and algebraic combinatorics, 1994 : DIMACS workshop, May 23-27, 1994 = Séries formelles et combinatoire algébrique, 1994	1996	Louis J. Billera Dimacs
+	The combinatorics of permutation polytopes	1995	Louis J. Billera A. Sarangarajan
+	Formal Power Series and Algebraic Combinatorics (Séries Formelles et Combinatoire Algébrique), 1994	1995	Louis J. Billera Curtis Greene Rodica Simion Richard P. Stanley
+	Iterated fiber polytopes	1994	Louis J. Billera Bernd Sturmfels
+ PDF Chat	Cellular strings on polytopes	1994	Louis J. Billera Mikhail Kapranov Bernd Sturmfels
+	Duality and Minors of Secondary Polyhedra	1993	Louis J. Billera I. M. Gel'fand Bernd Sturmfels
+	Fiber Polytopes	1992	Louis J. Billera Bernd Sturmfels
+	Modules of piecewise polynomials and their freeness	1992	Louis J. Billera Lauren L. Rose
+	Constructions and complexity of secondary polytopes	1990	Louis J. Billera P. Filliman Bernd Sturmfels
+	The algebra of continuous piecewise polynomials	1989	Louis J. Billera
+	Gröbner Basis Methods for Multivariate Splines	1989	Louis J. Billera Lauren L. Rose
+	The Stanley decomposition of the harmonic oscillator	1988	Louis J. Billera Richard Cushman Jan A. Sanders
+ PDF Chat	Homology of Smooth Splines: Generic Triangulations and a Conjecture of Strang	1988	Louis J. Billera
+ PDF Chat	Balanced subdivision and enumeration in balanced spheres	1987	Louis J. Billera Katherine Eberhardt Magurn
+ PDF Chat	Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets	1985	Margaret M. Bayer Louis J. Billera
+	Triangulations of Oriented Matroids and Convex Polytopes	1984	Louis J. Billera Beth Spellman Munson
+	Polarity and Inner Products in Oriented Matroids	1984	Louis J. Billera Beth Spellman Munson
+	Oriented Matroids and Triangulations of Convex Polytopes	1984	Louis J. Billera Beth Spellman Munson
+	Polyhedral Theory and Commutative Algebra	1983	Louis J. Billera
+	Leontief Substitution Systems and Matroid Complexes	1982	J. Scott Provan Louis J. Billera
+	The Numbers of Faces of Polytope Pairs and Unbounded Polyhedra	1981	Louis J. Billera Carl W. Lee
+	A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes	1981	Louis J. Billera Carl W. Lee
+	Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra	1980	J. Scott Provan Louis J. Billera
+ PDF Chat	Sufficiency of McMullen’s conditions for 𝑓-vectors of simplicial polytopes	1980	Louis J. Billera Carl W. Lee
+	A DECOMPOSITION PROPERTY FOR SIMPLICIAL COMPLEXES AND ITS RELATION TO DIAMETERS AND SHELLINGS	1979	Louis J. Billera J. Scott Provan
+	Pareto Surfaces of Complexity 1	1976	Louis J. Billera Robert E. Bixby
+	Topologies for 2 x ; Set-Valued Functions and their Graphs	1971	Louis J. Billera
+	Topologies for $2\sp{x}$; set-valued functions and their graphs	1971	Louis J. Billera

Common Coauthors

Coauthor	Papers Together
J. Scott Provan	6
Bernd Sturmfels	5
Samuel K. Hsiao	5
Stephanie van Willigenburg	4
Susan Holmes	3
Eran Nevo	3
Karen Vogtmann	3
Richard Ehrenborg	3
Karola Mészáros	3
Gábor Hetyei	3
Persi Diaconis	3
Saúl A. Blanco	3
Carl W. Lee	3
Lionel Levine	3
Victor Reiner	3
Beth Spellman Munson	3
Hugh Thomas	2
Aravamuthan Sarangarajan	2
Margaret Readdy	2
Eric Babson	2
Lauren L. Rose	2
Francesco Brenti	2
Ning Jia	2
Ning Jia	1
Kenneth S. Brown	1
Curtis Greene	1
I. M. Gel'fand	1
Dimacs	1
Katherine Eberhardt Magurn	1
Justin Tatch Moore	1
Robert E. Bixby	1
Clara S. Chan	1
Kristin A. Camenga	1
Megan Owen	1
Rodica Simion	1
S. A. Walker	1
Anders Björner	1
Kenneth S. Brown	1
Mikhail Kapranov	1
Y. Wang	1
P. Filliman	1
Niandong Liu	1
Richard Cushman	1
Kenneth S. Williams	1
Amy N. Myers	1
Jan A. Sanders	1
Vasu Tewari	1
Richard P. Stanley	1
C. Dufort Moraites	1
Margaret M. Bayer	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets	1985	Margaret M. Bayer Louis J. Billera	14
+	Enumerative Combinatorics	1997	Richard P. Stanley Gian‐Carlo Rota	13
+	The number of faces of a simplicial convex polytope	1980	Richard P. Stanley	12
+	Combinatorics and Commutative Algebra	1996	Richard P. Stanley	11
+	A new basis of polytopes	1988	Gil Kalai	11
+	On Posets and Hopf Algebras	1996	Richard Ehrenborg	10
+ PDF Chat	Generalized $H$-Vectors, Intersection Cohomology of Toric Varieties, and Related Results	2018	Richard P. Stanley	10
+	Flagf-vectors and thecd-index	1994	Richard P. Stanley	10
+ PDF Chat	None	2000	Louis J. Billera Niandong Liu	9
+	The cd-Index of Zonotopes and Arrangements	1998	Louis J. Billera Richard Ehrenborg Margaret Readdy	9
+ PDF Chat	A new index for polytopes	1991	Margaret M. Bayer Andrew Klapper	9
+ PDF Chat	Face Numbers of Polytopes and Complexes	2004	Louis J. Billera Anders Björner	8
+	A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes	1981	Louis J. Billera Carl W. Lee	8
+ PDF Chat	Balanced Cohen-Macaulay complexes	1979	Richard P. Stanley	8
+	Facing up to arrangements: face-count formulas for partitions of space by hyperplanes	1975	Thomas Zasĺavsky	8
+ PDF Chat	None	1998	Richard Ehrenborg Margaret Readdy	8
+	The Upper Bound Conjecture and Cohen-Macaulay Rings	1975	Richard P. Stanley	7
+ PDF Chat	Combinatorial Hopf algebras and generalized Dehn–Sommerville relations	2006	Marcelo Aguiar Nantel Bergeron Frank Sottile	7
+ PDF Chat	Enriched 𝑃-Partitions	1997	John R. Stembridge	7
+	Monotonicity of the cd-index for polytopes	2000	Louis J. Billera Richard Ehrenborg	7
+	Convex polytopes and the upper bound conjecture	1971	Peter McMullen G. C. Shephard J. E. Reeve Alan Ball	7
+	Thec-2d-Index of Oriented Matroids	1997	Louis J. Billera Richard Ehrenborg Margaret Readdy	7
+	Cohen-Macaulay Complexes	1977	Richard P. Stanley	6
+	The maximum numbers of faces of a convex polytope	1970	Peter McMullen	6
+ PDF Chat	A Combinatorial Analogue of Poincaré's Duality Theorem	1964	Victor Klee	6
+	Lectures on Polytopes	1994	Günter M. Ziegler	6
+	A generalized lower‐bound conjecture for simplicial polytopes	1971	Peter McMullen David W. Walkup	5
+	The numbers of faces of simplicial polytopes	1971	Peter McMullen	5
+ PDF Chat	Sufficiency of McMullen’s conditions for 𝑓-vectors of simplicial polytopes	1980	Louis J. Billera Carl W. Lee	5
+	Noncommutative Symmetrical Functions	1995	Israel M. Gelfand D. Krob Alain Lascoux Bruno Leclerc Vladimir Retakh Jean-Yves Thibon	5
+	Hilbert functions of graded algebras	1978	Richard P. Stanley	5
+ PDF Chat	Intersection homology of toric varieties and a conjecture of Kalai	1999	Tom Braden Robert MacPherson	5
+	Flag Vectors of Eulerian Partially Ordered Sets	2001	Margaret M. Bayer Gábor Hetyei	5
+	Constructions and complexity of secondary polytopes	1990	Louis J. Billera P. Filliman Bernd Sturmfels	5
+	The toric ℎ-vectors of partially ordered sets	2000	Margaret M. Bayer Richard Ehrenborg	5
+	A Survey of Eulerian Posets	1994	Richard P. Stanley	4
+	Cohen-Macaulay quotients of polynomial rings	1976	Gerald Allen Reisner	4
+	Peak quasisymmetric functions and Eulerian enumeration	2003	Louis J. Billera Samuel K. Hsiao Stephanie van Willigenburg	4
+	Fiber Polytopes	1992	Louis J. Billera Bernd Sturmfels	4
+	Enumerative Combinatorics	1986	Richard P. Stanley	4
+ PDF Chat	On lexicographically shellable posets	1983	Anders Björner Michelle L. Wachs	4
+	Linear inequalities for flags in graded posets	1997	Louis J. Billera Gábor Hetyei	4
+ PDF Chat	Lawrence Polytopes	1990	Margaret M. Bayer Bernd Sturmfels	4
+	The Numbers of Faces of Polytope Pairs and Unbounded Polyhedra	1981	Louis J. Billera Carl W. Lee	4
+ PDF Chat	Polytope pairs and their relationship to linear programming	1974	Victor Klee	4
+	Noncommutative Pieri Operators on Posets	2000	Nantel Bergeron Stefan Mykytiuk Frank Sottile Stephanie van Willigenburg	4
+ PDF Chat	Bier Spheres and Posets	2004	Anders Björner Andreas Paffenholz Jonas Sjöstrand Günter M. Ziegler	4
+	THE GEOMETRY OF TORIC VARIETIES	1978	V. I. Danilov	4
+	Enumerative Combinatorics	1999	Richard P. Stanley Sergey Fomin	3
+	A combinatorial abstraction of linear programming	1977	Robert G. Bland	3