We show that the membership problem in a finitely generated submonoid of a graph group (also called a right-angled Artin group or a free partially commutative group) is decidable if and only if the independence graph (commutation graph) is a transitive forest. As a consequence we obtain the first example of a finitely presented group with a decidable generalized word problem that does not have ...

Motivated by the study of decipherability conditions for codes weaker than Unique Decipherability (UD), we introduce the notion of coding partition. Such a notion generalizes that of UD code and, for codes that are not UD, allows to recover the “unique decipherability” at the level of the classes of the partition. By tacking into account the natural order between the partitions, we define the c...

A cooperative game with transferable utilities, or simply a TU-game, describes a situation in which players can obtain certain payo®s by cooperation. A solution mapping for these games is a mapping which assigns to every game a set of payo® distributions over the players in the game. Well-known solution mappings are the Core and the Weber set. In this paper we consider the mapping assigning to ...

For a positive integer $N$ and $\mathbb{A}$, subset of $\mathbb{Q}$, let $\mathbb{A}$-$\mathcal{KS}(N)$ denote the set $\alpha=\dfrac{\alpha_{1}}{\alpha_{2}}\in \mathbb{A\setminus} \{0,N\}$, where $\alpha_{2}r-\alpha_{1}$ divides $\alpha_{2}N-\alpha_{1}$ for every prime divisor $r$ $N$. The is called $N$-Korselt bases in $\mathbb{A}$. Let $p, q$ be two distinct numbers. In this paper, we prove ...

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...