Related papers: On Quasi Ordinal Diagram Systems

This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of rooted connected chord diagrams is further studied and new…

In this paper, we investigate diagrams, namely functors from any small category to a fixed category, and more particularly, their bisimilarity. Initially defined using the theory of open maps of Joyal et al., we prove several equivalent…

Generalized Higman's Theorem is the direct counterpart of Higman's Theorem that asserts the closure of the class of \emph{better} quasi-orders, instead of the class of \emph{well} quasi-orders, under the construction $P\mapsto P^{<\omega}$…

We provide a method of constructing better-quasi-orders by generalising a technique for constructing operator algebras that was developed by Pouzet. We then generalise the notion of $\sigma$-scattered to partial orders, and use our method…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

The regularity lemma of Szemeredi asserts that one can partition every graph into a bounded number of quasi-random bipartite graphs. In some applications however, one would like to have a strong control on how quasi-random these bipartite…

Proof terms are syntactic expressions that represent computations in term rewriting. They were introduced by Meseguer and exploited by van Oostrom and de Vrijer to study equivalence of reductions in (left-linear) first-order term rewriting…

This ongoing project aims to define and investigate, from the standpoint of category theory, order theory and universal algebra, the notions of higher-order many-sorted rewriting system and of higher-order many-sorted categorial algebra and…

We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…

We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…

Let $W$ be a finite Coxeter group and $\Omega$ be its $W$-graph algebra as defined by Gyoja. The author's previous paper \cite{hahn2016wgraphs} considered this algebra in some detail, proposed, and proved in some small cases the $W$-graph…

In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…

We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

This paper studies the structure of graphs with given tree-width and excluding a fixed complete bipartite subgraph, which generalises the bounded degree setting. We give a new structural description of such graphs in terms of so-called…

We establish the connection between the Steinitz problem for ordering vector families in arbitrary norms and its variant for not necessarily zero-sum families consisting of `nearly unit' vectors.

In the present paper we propose a new approach on `distributed systems': the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations…

In contrast to the abundance of "direct" Ramsey results for classes of finite structures (such as finite ordered graphs, finite ordered metric spaces and finite posets with a linear extension), in only a handful of cases we have a…

We present an extension of the Angluin-style learning algorithm for tree automata that incorporates deductive inference. The learning algorithm is provided with a term rewriting system that specifies properties of the target tree language…