Jose Bastidas

Research

My research interests lie in algebraic combinatorics. I am specially interested in the interplay between Hopf monoids in the category of Species and hyperplane arrangements.

See my papers on arXiv.

Papers and preprints

• Ornamentation lattices and intreeval hypergraphic lattices (with A. Abram, F. Gélinas, V. Pilaud, A. Sack)
  In preparation

• Flow polytopes of graphs with cycles and locally gentle algebras (with A. Abram, B. Dequêne, A. Morales, G. Park, H. Thomas)
  In preparation

• Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements (with S. Brauner, M. Guay-Paquet, A. Morales, G. Park, F. Saliola)
  [arXiv preprint]

• The h*-polynomials of type C hypersimplices (with A. Abram)
  [arXiv preprint]

• Left Regular Bands of Groups and the Mantaci--Reutenauer algebra (with S. Brauner, F. Saliola)
  Journal of Algebra, Volume 655, 2024.
  [DOI] [arXiv version]

• The Primitive Eulerian polynomial (with C. Hohlweg, F. Saliola)
  Combinatorial theory, Volume 4, Issue 1, 2024.
  [DOI] [arXiv version]

• Type B species and bimonoids (with M. Aguiar)
  In preparation

• The polytope algebra of generalized permutahedra
  Algebraic Combinatorics, Volume 4 (2021) no. 5, pp. 909-946.
  [DOI] [arXiv version]

• Associahedra, cyclohedra and inversion of power series (with M. Aguiar)
  [arXiv preprint]

• Characteristic elements for real hyperplane arrangements and deformations of the braid arrangement (with M. Aguiar, S. Mahajan)
  In preparation

Conference proceedings

• (Extended abstract) The h*-polynomials of type C hypersimplices (with A. Abram)
  To appear in Séminaire Lotharingien de Combinatoire XX (2025) Article #77, 12 pp.

• (Extended abstract) The polytope algebra of generalized permutahedra
  Séminaire Lotharingien de Combinatoire 85B (2021) Article #61, 12 pp.

• (Extended abstract) Characteristic elements for real hyperplane arrangements (with M. Aguiar, S. Mahajan)
  Séminaire Lotharingien de Combinatoire 82B (2019) Article #60, 12 pp.

Book Chapters

• Hopf monoids and polynomial invariants of combinatorial structures (with M. Aguiar)
  To appear in Algebraic and Geometric Combinatorics - Cambridge University Press (Editors: F. Ardila, C. Benedetti, A. Morales)

Theses

• Species and Hyperplane Arrangements
  Ph.D. Cornell University, 2021.

• Cox Rings of Big, Nef and Effective Rational Surfaces
  M.Sc. Universidad de los Andes, 2014.