Bisymmetric and quasitrivial operations: characterizations and enumerations

نویسنده

  • Jimmy Devillet
چکیده

We investigate the class of bisymmetric and quasitrivial binary operations on a given set X and provide various characterizations of this class as well as the subclass of bisymmetric, quasitrivial, and order-preserving binary operations. We also determine explicitly the sizes of these classes when the set X is finite.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quasitrivial semigroups: characterizations and enumerations

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer seq...

متن کامل

The least-square bisymmetric solution to a quaternion matrix equation with applications

In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necess...

متن کامل

Alternative Axiomatic Characterizations of the Grey Shapley Value

The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapl...

متن کامل

Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition

Forbidden characterizations may sometimes be the most natural way to describe families of graphs, and yet these characterizations are usually very hard to exploit for enumerative purposes. By building on the work of Gioan and Paul (2012) and Chauve et al. (2014), we show a methodology by which we constrain a split-decomposition tree to avoid certain patterns, thereby avoiding the corresponding ...

متن کامل

Two iterative algorithms to compute the bisymmetric solution of the matrix equation

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem ‖ ∑l i=1 AiX̂iBi− C‖F = minXi∈BRni×ni‖ ∑l i=1 AiXiBi−C‖F and the matrix nearness problem [X̂1, X̂2, ..., X̂l] = min[X1,X2,...,Xl]∈SE ‖[X1, X2, ..., Xl] − [X̃1, X̃2, ..., X̃l]‖F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution s...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/1712.07856  شماره 

صفحات  -

تاریخ انتشار 2017