Selected (or Recent) Publications - L.J. Billera
Billera, L. J., and C. W. Lee, A proof of the sufficiency of McMullen's conditions for
f
-vectors of simplicial convex polytopes,
Journal of Combinatorial Theory
Series A
31
(1981), 237-55.
Billera, L. J., and M. M. Bayer, Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets,
Inventiones Mathematicae
79
(1985), 143-57.
Billera, L. J., Homology of smooth splines: Generic triangulations and a conjecture of Strang,
Transactions of the American Mathematical Society
310
(1988), 325-40.
Billera, L. J., R. Cushman, and J. A. Sanders, The Stanley decomposition of the harmonic oscillator,
Proceedings of the Koninklijke Nederlandse Academie von Wetenschappen
, series A,
91
(1988), 375-93.
Billera, L. J., The algebra of continuous piecewise polynomials.
Advances in Mathematics
76
(1989), 170-83.
Billera, L. J., and L. L. Rose, Grobner basis methods for multivariate splines. In
Mathematical methods in computer aided geometric design,
ed. T. Lyche and L. L. Schumaker, pp. 93-104. Academic Press, New York, 1989.
Billera, L. J. and B. Sturmfels, Fiber polytopes.
Annals of Mathematics
135
(1992), 527-49.
Billera, L. J. and A. Sarangarajan, All 0-1 polytopes are traveling salesman polytopes.
Combinatorica
16
(1996), 175-188.
Babson, E., L.J. Billera and C. Chan,
Neighborly Cubical Spheres and a Cubical Lower Bound Conjecture
,
Israel Jour. Math.
102
(1997) 297-315
Billera, L. J. and A. Bjorner,
Face Numbers of Polytopes and Complexes
,
Handbook of Discrete and Computational Geometry
, J.E.~Goodman and J.~O'Rourke, eds., CRC Press, Boca Raton, New York, 1997, pp. 291-310.
Billera, L. J., R. Ehrenborg and M. Readdy, The
c
-2
d
-index of oriented matroids,
J. Comb. Theory
, Series A,
80
(1997), 79-105.
Babson, E. and L.J. Billera,
The geometry of products of minors
,
Discrete and Computational Geometry
20
(1998), 231-249.
Billera, L. J., R. Ehrenborg and M. Readdy,
The
cd
-index of zonotopes and arrangements
,
Mathematical Essays in Honor of Gian-Carlo Rota
, B. Sagan and R. Stanley, eds., Birkhauser, Boston, 1998.
Billera, L.J., K.S. Brown and P. Diaconis,
Random walks and plane arrangements in three dimensions
,
American Mathematical Monthly
106
(1999), 502-524.
Billera, L. J. and G. Hetyei,
Linear inequalities for flags in graded partially ordered sets
,
Journal of Combinatorial Theory
, Series A,
89
(2000), 77-104.
arXiv:math.CO/9706220
Billera, L. J. and R. Ehrenborg,
Monotonicity of the
cd
-index for polytopes
,
Mathematische Zeitschrift
233
(2000), 421-441.
Billera, L. J. and N. Liu,
Noncommutative enumeration in graded posets
,
Journal of Algebraic Combinatorics
12
(2000), 7-24.
Billera, L. J. and G. Hetyei,
Decompositions of partially ordered sets
,
Order
17
(2000), 141-166.
Billera, L. J., S. Holmes and K. Vogtmann,
Geometry of the space of phylogenetic trees
,
Advances in Applied Math.
27
(2001) 733-767.
Billera, L.J. and P. Diaconis,
A geometric interpretation of the Metropolis-Hastings algorithm
,
Statistical Science
16
(2001), 335-339.
Billera, L.J., S.K. Hsiao and S. van Willigenburg,
Peak Quasisymmetric Functions and Eulerian Enumeration
,
Advances in Mathematics
176
(2003), 248-276.
Billera, L.J., H. Thomas and S. van Willigenburg,
Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions
, arXiv:math.CO/0405434, 23 May 2004, revised 19 May, 2005. In
Advances in Mathematics
204
(2006), 204-240.
Billera, L.J., S.K. Hsiao and J.S. Provan,
Enumeration in convex geometries and associated polytopal subdivisions of spheres
, arXiv:math.CO/0505576, 26 May 2005. In
Discrete and Computational Geometry
39
(2008), 123-137.
Billera, L.J., N. Jia and V. Reiner,
A quasisymmetric function for matroids
, arXiv:math.CO/0606646, 26 June 2006. In
European Journal of Combinatorics
30
(2009), 1727-1757.
Billera, L.J., and F. Brenti,
Quasisymmetric functions and Kazhdan-Lusztig polynomials
,
Israel Jour. Math.
184
(2011), 317-348. Also arXiv:0710.3965, 22 October 2007.
Billera, L.J.,
Flag enumeration in polytopes, Eulerian partially ordered set and Coxeter groups
,
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)
, Hyderabad, India, Volume 4: Invited Lectures, Rajendra Bhatia, Editor, World Scientific, 2010, pp. 2389-2415. Slides for the corresponding
ICM lecture
.
Billera, L.J. and E. Nevo,
Nonpolytopal nonsimplicial lattice spheres with nonnegative toric g-vector
,
Discrete and Computational Geometry
48
(2012), 1048-1057. Also arXiv:1110.0739, 4 Oct 2011.
Billera, L.J., J. Moore, C. Moraites, Y. Wang and K. Williams,
Maximal unbalanced families
, arXiv:1209.2309 [math.CO], 11 Sep 2012.
Billera, L.J. and S. Blanco, Bandwidth of the product of paths of the same length,
Discrete Applied Mathematics
161
(2013), 3080-3086. Also
arXiv:1209.3201
Billera, L.J., L. Levine, K. Meszaros, How to decompose a permutation into a pair of labeled Dyck paths by playing a game,
Proceedings of the American Mathematical Society
143
(2015), 1865-1873. Also
arXiv:1306.6744
, 28 June, 2013.
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Last update: March, 2015