An Explicit Derivation of the Möbius Function for Bruhat Order

نویسنده

  • Brant C. Jones
چکیده

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.

برای دانلود 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

A short derivation of the Möbius function for the Bruhat order

We give a short, self-contained derivation of the Möbius function for the Bruhat orderings of Coxeter groups and their parabolic quotients.

متن کامل

A Weighted Enumeration of Maximal Chains in the Bruhat Order

Given a finite Weyl group W with root system , assign the weight α ∈ to each covering pair in the Bruhat order related by the reflection corresponding to α. Extending this multiplicatively to chains, we prove that the sum of the weights of all maximal chains in the Bruhat order has an explicit product formula, and prove a similar result for a weighted sum over maximal chains in the Bruhat order...

متن کامل

On a Bruhat-like Poset

We investigate the combinatorics and the topology of the poset of strata of a Schubert like stratification on the Grassmannian of hermitian lagrangian spaces in Cn ⊕ Cn. We prove that this poset is a modular complemented lattice, we compute its Möbius function and we investigate the combinatorics and the topology of its order intervals.

متن کامل

From the Weak Bruhat Order to Crystal Posets

We investigate the ways in which fundamental properties of the weak Bruhat order on a Weyl group can be lifted (or not) to a corresponding highest weight crystal graph, viewed as a partially ordered set; the latter projects to the weak order via the key map. First, a crystal theoretic analogue of the statement that any two reduced expressions for the same Coxeter group element are related by Co...

متن کامل

Comprehensive Simulation for Two-diode Model of Photovoltaic Cells in SimPowerSystems Using Explicit Mathematical Functions

In this paper, using Thevenin’s theorem and also nonlinear Lambert W function, a novel two-diode model of photovoltaic cells is presented in mathematical explicit manner. In comparison with existing explicit models in the literature which are valid exclusively for n2=n1 and n2=2n1, this model includes a wide range of silicon-based cells with arbitrary diodes ideality factors. Acquiring regulati...

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

برای دانلود 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

عنوان ژورنال:
  • Order

دوره 26  شماره 

صفحات  -

تاریخ انتشار 2009