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-2d-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