Related papers: A Ring structure on the Class of Combinatorial Gam…
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…
We consider the abstract structure of the monoid M of mis\`ere impartial game values. Several new results are presented, including a proof that the group of fractions of M is almost torsion-free; a method of calculating the number of…
A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are…
A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality…
In this paper we describe the ideal category of a ring R as preadditive proper category. Further it is also shown that the cones in this category is a ring with appropriate addition and multiplication.
We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an…
We introduce a new combinatorial game, named Triangle Game. In this game, a directed $3$-cycle graph is given, and tokens are placed on each vertex. The player chooses an edge and takes at least one token from the initial vertex. At the…
Let A be a class of objects, equipped with an integer size such that for all n the number a(n) of objects of size n is finite. We are interested in the case where the generating fucntion sum_n a(n) t^n is rational, or more generally…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
In this paper we provide a complete algebraic characterization of elementary equivalence of rings with a finitely generated additive group in the language of pure rings. The rings considered are arbitrary otherwise.
For an arbitrary category, we consider the least class of functors con- taining the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of…
In recent years methods have been proposed to extend classical game theory into the quantum domain. This paper explores further extensions of these ideas that may have a substantial potential for further research. Upon reformulating quantum…
In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If…
In general the endomorphisms of a non-abelian group do not form a ring under the operations of addition and composition of functions. Several papers have dealt with the ring of functions defined on a group which are endomorphisms when…
Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction…
Game semantics has provided adequate models for a variety of programming languages, in which types are interpreted as two-player games and programs as strategies. Melli\`es (2018) suggested that such categories of games and strategies may…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
Conways Game of Life is a cellular automaton noted for its rich, complex, and emergent behavior, which seems qualitatively lifelike it exists within a wider space of different rule-sets of cellular automata none of which have been found to…
The paper discusses coordination games with remote players that have access to an entangled quantum state. It shows that the entangled state cannot be used by players for communicating information, but that in certain games it can be used…
Let $R$ be an associative ring with identity and let $N$ be a nil ideal of $R$. It is shown that units of $R/N$ can be lifted to units in $R$. Under some mild conditions on the ring, a procedure is given to determine those lifted units in a…