the probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. here we illustrate that a wider context may be considered and show some structural restrictions on the group.

Reasoning about commutativity between data-structure operations is an important problem with applications including parallelizing compilers, optimistic parallelization and, more recently, Ethereum smart contracts. There have been research results on automatic generation of commutativity conditions, yet we are unaware of any fully automated technique to generate conditions that are both sound an...

Reasoning about commutativity between data-structure operations has been, and remains, an important problem with applications including parallelizing compilers, optimistic parallelization and, more recently, Ethereum smart contracts. There have been research results on automatic generation of commutativity conditions, yet we are unaware of any fully automated technique to generate conditions th...

Leading order study of direct photon production from proton–proton collisions, in the framework Minimal (Seiberg–Witten) Non-Commutative Standard Model (NCSM), taking into account Earth-rotation effects. We found that relative non-commutative contributions increase significantly at very high transverse momentum. Therefore, using Run-1 ([Formula: see text] TeV) and Run-2 ATLAS experimental data ...

Traditional analysis and usage of operation commutativity relies on pairwise commutativity relationships. In contrast, this paper presentsmethod group commutativity, which specifies the conditions under which operations in amethod group will commute. Method group commutativity can be practically applied to efficiently support distributed object caching and concurrency control. A formal definiti...

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second r...

Information flow security ensures that the secret data manipulated by a program does not influence its observable output. Proving information is especially challenging for concurrent programs, where operations on may execution time of thread and, thereby, interleaving between different threads. Such internal timing channels affect outcome even if an attacker observe times. Existing verification...

Let P2(G) be defined as the probability that any two elements selected at random from the group G, commute with one another. If G is an Abelian group, P2(G) = 1, so our interest lies in the properties of the commutativity of nonAbelian groups. Particular results include that the maximum commutativity of a non-Abelian group is 5/8, and this degree of commutativity only occurs when the order of t...