Möbius functions and confluent semi-commutations

Rewriting, Möbius Functions and Semi-Commutations

Closure of regular languages under semi-commutations

The closure of a regular language under a [partial, semi-] commutation I has been extensively studied. We present new advances on two problems of this area: (1) When is the closure of a regular language under [partial, semi-] commutation still regular? (2) Are there any robust classes of languages closed under [partial, semi-] commutation? We show that the class Pol(G) of polynomials of group l...

Lattices, Möbius Functions and Communication Complexity

In a recent paper, Hajnal, Maass and Tura'n analyzed the communication complexity of graph connectivity. Building on this work, we develop a general framework for the study of a broad class of communication problems which has several interesting special cases including the graph connectivity problem. The approach is based on combinatorial lattice theory.

Möbius functions and semigroup representation theory

This paper explores several applications of Möbius functions to the representation theory of finite semigroups. We extend Solomon’s approach to the semigroup algebra of a finite semilattice via Möbius functions to arbitrary finite inverse semigroups. This allows us to explicitly calculate the orthogonal central idempotents decomposing an inverse semigroup algebra into a direct product of matrix...

Determinants and Möbius functions in trace monoids

We show that the independence relation deening a trace monoid M admits a transitive orientation if and only if the characteristic series of a lexicographic cross section of M satisses an equation of the form Det(Id ? X) = 1, where X is a matrix representing the minimum nite automaton recognizing and Id is the identity matrix. This implies that, if the independence relation of a trace monoid M a...