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A review on the Eulerian ideal of a graph and its regularity
Speaker: Gonçalo Varejão (CMUC, UC|UP PhD student)
Over the past fifty years, a trend in commutative algebra has been to explore families of homogeneous ideals, in the polynomial ring, linked to various combinatorial structures, such as graphs, hypergraphs and simplicial complexes.In this presentation, we focus on the Eulerian ideal of a...

A characterization of one-element commutation classes
Speaker: Diogo Soares (CMUC, UC|UP PhD student)
A reduced word for a permutation of the symmetric group is its own commutation class if it has no commutation moves available. These words have the property that every factor of length 2 is formed by consecutive integers, but in general words of this form may not be reduced.  In this...

An adjoint theorem for finitary functors
Speaker: Lurdes Sousa (CMUC and IP Viseu)
A functor between locally presentable categories is a right adjoint iff it is accessible and preserves limits [1]. We prove that for a number of categories, called graduated, the preservation of countable limits is enough. Examples of graduated categories include sets, posets, Boolean...

Speaker: Aram Diaw (CMUP, Univ. Porto)

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