A short derivation of the Möbius function for the Bruhat order
نویسنده
چکیده
We give a short, self-contained derivation of the Möbius function for the Bruhat orderings of Coxeter groups and their parabolic quotients.
منابع مشابه
An Explicit Derivation of the Möbius Function for Bruhat Order
We give an explicit nonrecursive complete matching for the Hasse diagram of the strong Bruhat order of any interval in any Coxeter group. This yields a new derivation of the Möbius function, recovering a classical result due to Verma.
متن کاملFirst Principles Derivation of Displacement and Stress Function for Three-Dimensional Elastostatic Problems, and Application to the Flexural Analysis of Thick Circular Plates
In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...
متن کاملDerivation of Green’s Function for the Interior Region of a Closed Cylinder
The importance of constructing the appropriate Green function to solve a wide range of problems inelectromagnetics and partial differential equations is well-recognized by those dealing with classical electrodynamics and related fields. Although the subject of obtaining the Green function for certain geometries has been extensively studied and addressed in numerous sources, in this paper a syst...
متن کاملNon-linear Fractional-Order Chaotic Systems Identification with Approximated Fractional-Order Derivative based on a Hybrid Particle Swarm Optimization-Genetic Algorithm Method
Although many mathematicians have searched on the fractional calculus since many years ago, but its application in engineering, especially in modeling and control, does not have many antecedents. Since there are much freedom in choosing the order of differentiator and integrator in fractional calculus, it is possible to model the physical systems accurately. This paper deals with time-domain id...
متن کاملA combinatorial derivation of the Poincare' polynomials of the finite irreducible Coxeter groups
(1) The Poincar e polynomials of the nite irreducible Coxeter groups and the Poincar e series of the aane Coxeter groups on three generators are derived by an elementary combinatorial method avoiding the use of Lie theory and invariant theory. (2) Non-recursive methods for the computation of`standard reduced words' for (signed) permutations are described. The algebraic basis for both (1) and (2...
متن کامل