The Rearrangement Conjecture states that if two words over P are Wilf-equivalent in the factor order on P∗ then they are rearrangements of each other. We introduce the notion of strong Wilf-equivalence and prove that if two words over P are strongly Wilf-equivalent then they are rearrangements of each other. We further conjecture that Wilf-equivalence implies strong Wilf-equivalence. Résumé. La...

The purpose of this study was to investigate possible influences of pitch register and dynamic level on vibrato rates and widths of university and high school violin and viola players. Analysis showed that pitch register significantly affected the vibrato rates and widths of the performers. Musicians vibrated 0.32 Hz faster and approximately 26 cents wider during high pitches than during low pi...

There are two general irreversibility theorems for the renormalization group in more than two dimensions: the first one is of entropic nature, while the second one, by Forte and Latorre, relies on the properties of the stress-tensor trace, and has been recently questioned by Osborn and Shore. We start by establishing under what assumptions this second theorem can still be valid. Then it is comp...