Polytopes, Fibonacci numbers, Hopf algebras, and quasi-symmetric functions
Polytopes, Fibonacci numbers, Hopf algebras, and quasi-symmetric functions
In this paper we use the technique of Hopf algebras and quasi-symmetric functions to study the combinatorial polytopes. Consider the free abelian group $\mathcal{P}$ generated by all combinatorial polytopes. There are two natural bilinear operations on this group defined by a direct product $\times $ and a join $\divideontimes$ of …