On Isomorphism of Simplicial Complexes and Their Related Algebras

on isomorphism of simplicial complexes and their related algebras

On isomorphism of simplicial complexes and their related rings

In this paper, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphic as K-algebras. As a consequence, we show that two graphs are isomorphic if and only if their associated edge rings are isomorphic as K-algebras. Based on an explicit K-algebra isomorphism of two S...

Incidence algebras of simplicial complexes

With any locally finite partially ordered set K its incidence algebra Ω(K) is associated. We shall consider algebras over fields with characteristic zero. In this case there is a correspondence K ↔ Ω(K) such that the poset K can be reconstructed from its incidence algebra up to an isomorphism — due to Stanley theorem. In the meantime, a monotone mapping between two posets in general induces no ...

Combinatorial Hopf Algebras of Simplicial Complexes

We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these combinatorial Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their f -vectors. We al...

the impact of attending efl classes on the level of depression of iranian female learners and their attributional complexity

می توان گفت واقعیت چند لایه ا ی کلاس های زبان انگلیسی بسیار حائز اهمیت است، زیرا عواطف و بینش های زبان آموزان تحت تاثیر قرار می گیرد. در پژوهش پیش رو، گفته می شود که دبیران با در پیش گرفتن رویکرد فرا-انسانگرایی ، قادرند در زندگی دانش آموزانشان نقش مهمی را ایفا سازند. بر اساس گفته ی ویلیامز و بردن (2000)، برای کرل راجرز، یکی از بنیان گذاران رویکرد انسانگرایی ، یادگیری بر مبنای تجربه، نوعی از یاد...

Flows on Simplicial Complexes

Given a graph G, the number of nowhere-zero Zq-flows φG(q) is known to be a polynomial in q. We extend the definition of nowhere-zero Zq-flows to simplicial complexes ∆ of dimension greater than one, and prove the polynomiality of the corresponding function φ∆(q) for certain q and certain subclasses of simplicial complexes. Résumé. Et́ant donné une graphe G, on est connu que le nombre de Zq-flot...