Related papers: A generalization of Menon's identity

The ability to interpret the mental state of another agent based on its behavior, also called Theory of Mind (ToM), is crucial for humans in any kind of social interaction. Artificial systems, such as intelligent assistants, would also…

We present a first approximation of agent behaviour in a generalized model in contract theory. This model relaxes some of the the assumptions of one of the classical models allowing to include a broader range of agents. We introduce the…

We find limits of some multiple ergodic averages, generalizing a result of Bergelson to the setting of two commuting transformations and actions of amenable groups.

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

In previous articles we presented a simple set of axioms named Contexts, Systems and Modalities (CSM), where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a…

In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.

Motivated by some binomial coefficients identities encountered in our approach to the enumeration of convex polyominoes, we prove some more general identities of the same type, one of which turns out to be related to a strange evaluation of…

In this paper, we define new generalized k-Mersenne numbers and give a formula of generalized Mersenne polynomials and further we study their properties. Moreover, we define Gaussian Mersenne numbers and obtain some identities like Binet…

Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…

We generalize the definition of pseudo monomial characters and $M$-groups to the Brauer character and Isaacs' $\pi$-partial character settings. We prove an analogs of Isaacs's generalization of Taketa's theorem in those settings. We…

We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.

We prove several generalisations of the ping-pong lemma for negatively curved groups.

We provide an information-theoretic framework for studying the generalization properties of machine learning algorithms. Our framework ties together existing approaches, including uniform convergence bounds and recent methods for adaptive…

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.

We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.

It is well known that many famous Burnside-type problems have positive solutions for PI-groups and PI-algebras. In the present article we also consider various Burnside-type problems for PI-groups and PI-representations of groups.

Theory of Mind is commonly defined as the ability to attribute mental states (e.g., beliefs, goals) to oneself, and to others. A large body of previous work - from the social sciences to artificial intelligence - has observed that Theory of…

We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…

In this short note, we discuss the Barndorff-Nielsen lemma, which is a generalization of well-known Borel-Cantelli lemma. Although the result stated in the Barndorff-Nielsen lemma is correct, it does not follow from the argument proposed in…

Interest is growing in social learning models where users share opinions and adjust their beliefs in response to others. This paper introduces generalized-bias opinion models, an extension of the DeGroot model, that captures a broader range…