The Möbius function of generalized subword order

The Möbius function of generalized subword order

Let P be a poset and let P ∗ be the set of all finite length words over P . Generalized subword order is the partial order on P ∗ obtained by letting u ≤ w if and only if there is a subword u′ of w having the same length as u such that each element of u is less than or equal to the corresponding element of u′ in the partial order on P . Classical subword order arises when P is an antichain, whi...

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.

Power Function Distribution Characterized by Dual Generalized Order Statistics

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any rest...

Computing the Summation of the Möbius Function

A weighted Möbius function