50 citations · 250 across the 18 of their papers we have counts for
20 papers
Revisiting Generalizations of the Dehn--Sommerville Relations
Cesar Ceballos, Henri Mühle
We revisit several known versions of the Dehn--Sommerville relations in the context of: homology manifolds, semi-Eulerian complexes, general simplicial complexes, balanced semi-Eul…
- and -Triangles for -Associahedra
Cesar Ceballos, Henri Mühle
For any northeast path , we define two bivariate polynomials associated with the -associahedron: the - and the -triangle. We prove combinatorially that we can obtain on…
Elliptic and -Analogs of the Fibonomial Numbers
Nantel Bergeron, Cesar Ceballos, Josef Küstner
In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by it…
The Steep-Bounce Zeta Map in Parabolic Cataland
Cesar Ceballos, Wenjie Fang, Henri Mühle
As a classical object, the Tamari lattice has many generalizations, including -Tamari lattices and parabolic Tamari lattices. In this article, we unify these generalizations in…
Hopf dreams and diagonal harmonics
Nantel Bergeron, Cesar Ceballos, Vincent Pilaud
This paper introduces a Hopf algebra structure on a family of reduced pipe dreams. We show that this Hopf algebra is free and cofree, and construct a surjection onto a commutative…
Signature Catalan Combinatorics
Cesar Ceballos, Rafael S. González D'León
The Catalan numbers constitute one of the most important sequences in combinatorics. Catalan objects have been generalized in various directions, including the classical Fuss-Catal…
Geometry of -Tamari lattices in types and
Cesar Ceballos, Arnau Padrol, Camilo Sarmiento
In this paper, we exploit the combinatorics and geometry of triangulations of products of simplices to derive new results in the context of Catalan combinatorics of -Tamari latt…
Cluster Algebras of Type , Tropical Planes, and the Positive Tropical Grassmannian
Sarah B. Brodsky, Cesar Ceballos, Jean-Philippe Labbé
We show that the number of combinatorial types of clusters of type modulo reflection-rotation is exactly equal to the number of combinatorial types of tropical planes in $\ma…
A Hopf algebra of subword complexes
Nantel Bergeron, Cesar Ceballos
We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acycli…
Cluster algebras of type D: pseudotriangulations approach
Cesar Ceballos, Vincent Pilaud
We present a combinatorial model for cluster algebras of type in terms of centrally symmetric pseudotriangulations of a regular -gon with a small disk in the centre. This…
Combinatorics of the zeta map on rational Dyck paths
Cesar Ceballos, Tom Denton, Christopher R. H. Hanusa
An -Dyck path is a lattice path from to that stays above the line . The zeta map is a curious rule that maps the set of -Dyck path…
The diameter of type D associahedra and the non-leaving-face property
Cesar Ceballos, Vincent Pilaud
Generalized associahedra were introduced by S. Fomin and A. Zelevinsky in connection to finite type cluster algebras. Following recent work of L. Pournin in types and , this…
Fan realizations of subword complexes and multi-associahedra via Gale duality
Nantel Bergeron, Cesar Ceballos, Jean-Philippe Labbé
We present complete simplicial fan realizations of any spherical subword complex of type for . This provides complete simplicial fan realizations of simplicial multi…
Dyck path triangulations and extendability
Cesar Ceballos, Arnau Padrol, Camilo Sarmiento
We introduce the Dyck path triangulation of the cartesian product of two simplices . The maximal simplices of this triangulation are given by Dyck paths, and…
Denominator vectors and compatibility degrees in cluster algebras of finite type
Cesar Ceballos, Vincent Pilaud
We present two simple descriptions of the denominator vectors of the cluster variables of a cluster algebra of finite type, with respect to any initial cluster seed: one in terms o…
Acyclic systems of permutations and fine mixed subdivisions of simplices
Federico Ardila, Cesar Ceballos
A fine mixed subdivision of a (d-1)-simplex T of size n gives rise to a system of permutations of [n] on the edges of T, and to a collection of n unit (d-1)-simplic…
Realizing the associahedron: Mysteries and questions
Cesar Ceballos, Günter M. Ziegler
There are many open problems and some mysteries connected to the realizations of the associahedra as convex polytopes. In this note, we describe three -- concerning special realiza…
Many non-equivalent realizations of the associahedron
Cesar Ceballos, Francisco Santos, Günter M. Ziegler
Hohlweg and Lange (2007) and Santos (2004, unpublished) have found two different ways of constructing exponential families of realizations of the n-dimensional associahedron with n…
Subword complexes, cluster complexes, and generalized multi-associahedra
Cesar Ceballos, Jean-Philippe Labbé, Christian Stump
In this paper, we use subword complexes to provide a uniform approach to finite type cluster complexes and multi-associahedra. We introduce, for any finite Coxeter group and any no…
Three non-equivalent realizations of the associahedron
Cesar Ceballos, Günter M. Ziegler
We review three realizations of the associahedron that arise as secondary polytopes, from cluster algebras, and as Minkowski sums of simplices, and show that under any choice of pa…