30 citations · 30 across the 8 of their papers we have counts for
11 papers · 1 filter
Chromatic word-quasisymmetric functions of matroids
Raul Penaguiao, Sophie Rehberg
Billera, Jia, and Reiner (2009) introduced the quasisymmetric functions of matroids and showed that this defines a Hopf algebra homomorphism which is a valuative invariant, i.e., i…
The dimension of the feasible region of pattern densities
Frederik Garbe, Daniel Kral, Alexandru Malekshahian +1
A classical result of Erdős, Lovász and Spencer from the late 1970s asserts that the dimension of the feasible region of densities of graphs with at most k vertices in large graphs…
Lecture notes on algebraic methods in combinatorics
Raul Penaguiao
These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant…
Discrete signature varieties
Carlo Bellingeri, Raul Penaguiao
Discrete signatures are invariants computed from time series corresponding to the discretised version of the signature of paths. We study the algebraic varieties arising from their…
The tropical critical points of an affine matroid
Federico Ardila-Mantilla, Christopher Eur, Raul Penaguiao
We prove that the number of tropical critical points of an affine matroid (M,e) is equal to the beta invariant of M. Motivated by the computation of maximum likelihood degrees, thi…
Antipode formulas for pattern Hopf algebras
Raúl Penaguiao, Yannic Vargas
The permutation pattern Hopf algebra is a commutative filtered and connected Hopf algebra. Its product structure stems from counting patterns of a permutation, interpreting the coe…
The feasible regions for consecutive patterns of pattern-avoiding permutations
Jacopo Borga, Raul Penaguiao
We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family of permutations avoiding a fixed set of patterns…
The feasible region for consecutive patterns of permutations is a cycle polytope
Jacopo Borga, Raul Penaguiao
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called f…
Pattern Hopf algebras
Raul Penaguiao
This is a study on pattern Hopf algebras in combinatorial structures. We introduce the notion of combinatorial presheaf, by adapting the algebraic framework of species to the study…
The feasible region for consecutive patterns of permutations is a cycle polytope
Jacopo Borga, Raul Penaguiao
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the limit of such proportions on large permutations forms a region, called \emph{feas…
The kernel of chromatic quasisymmetric functions on graphs and hypergraphic polytopes
Raul Penaguiao
We study the chromatic symmetric function on graphs, and show that its kernel is spanned by the modular relations. We generalize this result to the chromatic quasisymmetric functio…