More Like this

1. Collision Avoidance Using Spherical Harmonics

   https://doi.org/10.1016/j.ifacol.2021.11.266  

   Patrick, Steven D.; Bakolas, Efstathios (January 2021, IFAC-PapersOnLine)
2. Avoidance of Self during CRISPR Immunization

   https://doi.org/10.1016/j.tim.2020.02.005  

   Weissman, Jake L.; Stoltzfus, Arlin; Westra, Edze R.; Johnson, Philip L.F. (July 2020, Trends in Microbiology)

   null (Ed.)
3. Avoidance couplings on non‐complete graphs

   https://doi.org/10.1002/rsa.20999  

   Bates, Erik; Podder, Moumanti (August 2021, Random Structures & Algorithms)

   Abstract A coupling of random walkers on the same finite graph, who take turns sequentially, is said to be anavoidance couplingif the walkers never collide. Previous studies of these processes have focused almost exclusively on complete graphs, in particular how many walkers an avoidance coupling can include. For other graphs, apart from special cases, it has been unsettled whether even two noncolliding simple random walkers can be coupled. In this article, we construct such a coupling on (i) anyd‐regular graph avoiding a fixed subgraph depending ond; and (ii) any square‐free graph with minimum degree at least three. A corollary of the first result is that a uniformly random regular graph onnvertices admits an avoidance coupling with high probability. 

   more » « less
4. Spherical Schubert varieties and pattern avoidance

   https://doi.org/10.1007/s00029-022-00760-8  

   Gaetz, Christian (April 2022, Selecta Mathematica)
5. Key-avoidance for alternating sign matrices

   https://doi.org/10.46298/dmtcs.14058  

   Bouvel, Mathilde; Smith, Rebecca; Striker, Jessica (March 2025, Discrete Mathematics & Theoretical Computer Science)

   We initiate a systematic study of key-avoidance on alternating sign matrices (ASMs) defined via pattern-avoidance on an associated permutation called the \emph{key} of an ASM. We enumerate alternating sign matrices whose key avoids a given set of permutation patterns in several instances. We show that ASMs whose key avoids $231$ are permutations, thus any known enumeration for a set of permutation patterns including $231$ extends to ASMs. We furthermore enumerate by the Catalan numbers ASMs whose key avoids both $312$ and $321$. We also show ASMs whose key avoids $312$ are in bijection with the gapless monotone triangles of [Ayyer, Cori, Gouyou-Beauchamps 2011]. Thus key-avoidance generalizes the notion of $312$-avoidance studied there. Finally, we enumerate ASMs with a given key avoiding $312$ and $321$ using a connection to Schubert polynomials, thereby deriving an interesting Catalan identity. Comment: 28 pages 

   more » « less