The nets considered here are an extension of Petri nets in two aspects. In the semantical aspect, there is no one firing rule common to all transitions, but every transition is treated as an operator on data stored in its entry places and return results in its exit places. A state (marking) is a mapping of places (variables) into a given data structure, while interpretation is a mapping of tran...

A given monoid usually admits many presentations by generators and relations the notion of Tietze equivalence characterizes when two describe same monoid: it is case one can transform presentation into other using families so-called transformations. The goal this article to provide an abstract geometrical understanding well-known fact, constructing a model structure on category presentations, i...

The commutative Hopf monoid of set compositions is a fundamental internal to vector species, having undecorated bosonic Fock space the combinatorial algebra quasisymmetric functions. We construct geometric realization this over adjoint (essentialized) braid hyperplane arrangement, which identifies monomial basis with signed characteristic functions interiors permutohedral tangent cones. show th...

Abstract The goal of this paper is to show that valuation theory and Hopf are compatible on the class generalized permutahedra. We prove structure $\textbf {GP}^+$ these polyhedra descends, modulo inclusion-exclusion relations, an indicator monoid $\mathbb {I}(\textbf {GP}^+)$ permutahedra isomorphic weighted ordered set partitions. This quotient cofree. It terminal object in category monoids w...

In this paper we are interested in the Chinese monoid and show that the Chinese monoid has complete rewriting system. Mathematics Subject Classification: 16S15; 20F05; 20F10; 20M50; 68Q42