4 papers
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 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…
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…