The set of synchronizing words a given n-state automaton forms regular language recognizable by an with \(2^n - n\) states. size recognizing for the is linked to computational problems related synchronization and length words. Hence, it natural investigate automata extremal this property, i.e., such that minimal deterministic has sync-maximal permutation groups have been introduced in [S. Hoffm...

Two matrix optimization problems are analyzed. These problems arise in signal processing and communication. In the first problem, the trace of the mean square error matrix is minimized, subject to a power constraint. The solution is the training sequence, which yields the best estimate of a communication channel. The solution is expressed in terms of the eigenvalues and eigenvectors of correlat...

Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...

Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce notion permutation resemblance a function, which looks to measure distance given map is from being permutation. We prove several results concerning permutation resemblance and show how it can ...