JavaFX 26 Today

The main goal of the project Math-Net.Ru is to collect scientific publications in Russian and Soviet mathematics journals since their foundation to today and the authors of these publications into a single database and to provide access to full-text articles for broad international mathematical community. Leading Russian mathematics journals have been comprehensively digitized dating back to the first volumes.

We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$. We then prove additional equivalences to explicitly classify all quasi-consecutive patterns of length $5$ into 26 Wilf-equivalence classes.

Scrambling the standard 3x3x3 Rubik's Cube corresponds to a random walk on a group containing approximately 43 quintillion elements. Viewing the random walk as a Markov chain, its mixing time determines the number of random moves required to sufficiently scramble a solved cube. With the aid of a supercomputer, we show that the mixing time is at least 26, providing the first non-trivial bound.