Related papers: Models with second order properties, V: A General …
Keller proposed a combinatorial conjecture on construction of an n-by-infinite matrix, which comes from showing the existence of many orbits of different sizes in certain linear group actions. He proved it for the case n=4, and we show that…
A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…
This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
Mobile agents research is clearly aiming towards imposing agent based development as the next generation of tools for writing software. This paper comes with its own contribution to this global goal by introducing a novel unifying framework…
We investigate properties of families $F$ of subsets of a finite set in a situation where subsets are incomparable by the binary inclusion relation and a) for any $A\notin F$, there is such set $A'\in F$ that either $A\subset A'$ or…
Let R be a commutative ring with unity, M be an unitary R-module and {\Gamma} be a simple graph. This research article is an interplay of combinatorial and algebraic properties of M . We show a combinatorial object completely determines an…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
We investigate the most general "phase space" of configurations, consisting of all possible ways of assigning elementary attributes, "energies", to elementary positions, "cells". We discuss how this space possesses structures that can be…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
In the combinatorial-action contract model (D\"utting et al., FOCS'21) a principal delegates the execution of a complex project to an agent, who can choose any subset from a given set of actions. Each set of actions incurs a cost to the…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We introduce a class of graphs called compound graphs, generalizing rectangles, which are constructed out of copies of a planar bipartite base graph. The main result is that the number of perfect matchings of every compound graph is…
A combinatorial theory of associative $n$-categories has recently been proposed, with strictly associative and unital composition in all dimensions, and the weak structure arising as a combinatorial notion of homotopy with a natural…
In applied game theory the motivation of players is a key element. It is encoded in the payoffs of the game form and often based on utility functions. But there are cases were formal descriptions in the form of a utility function do not…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not…
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…