6,209 research outputs found
Negation Switching Equivalence in Signed Graphs
Unless mentioned or defined otherwise, for all terminology and notion in graph theory the reader is refer to [8]. We consider only finite, simple graphs free from self-loops
Three Hopf algebras and their common simplicial and categorical background
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common frameworkPreprin
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