combinatorial hopf algebra
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Author(s):  
Marko Pesovic

For a hypergraphic polytope there is a weighted quasisymmetric function which enumerates positive integer points in its normal fan and determines its f-polynomial. This quasisymmetric function invariant of hypergraphs extends the Stanley chromatic symmetric function of simple graphs. We consider a certain combinatorial Hopf algebra of hypergraphs and show that universal morphism to quasisymmetric functions coincides with this enumerator function. We calculate the f-polynomial of uniform hypergraphic polytopes.



2018 ◽  
Vol 5 (1) ◽  
pp. 61-102 ◽  
Author(s):  
Imad Eddine Bousbaa ◽  
Ali Chouria ◽  
Jean-Gabriel Luque


2016 ◽  
Vol 453 ◽  
pp. 609-643 ◽  
Author(s):  
Luis A. Duffaut Espinosa ◽  
Kurusch Ebrahimi-Fard ◽  
W. Steven Gray




2013 ◽  
Vol 38 (4) ◽  
pp. 767-783 ◽  
Author(s):  
Carolina Benedetti


2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Jean-Baptiste Priez

International audience In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like monoids using polynomial realizations. Thank to this construction we reveal a lattice structure on those combinatorial Hopf algebras. As an application, we construct a new combinatorial Hopf algebra on binary trees with multiplicities and use it to prove a hook length formula for those trees. Dans une première partie, nous formalisons la construction d’algèbres de Hopf combinatoires à partir d’une réalisation polynomiale et de monoïdes de type monoïde plaxique. Grâce à cette construction, nous mettons à jour une structure de treillis sur ces algèbres de Hopf combinatoires. Comme application, nous construisons une nouvelle algèbre de Hopf sur des arbres binaires à multiplicités et on l’utilise pour démontrer une formule des équerressur ces arbres.



2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Rémi Maurice

Poster session International audience We investigate the combinatorial Hopf algebra based on uniform block permutations and we realize this algebra in terms of noncommutative polynomials in infinitely many bi-letters.





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