Abstract
AbstractWe survey Jean-Louis Loday’s vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry, and algebra. We present in particular four topics where it plays a central role: lattice congruences of the weak order and their quotientopes, cluster algebras and their generalized associahedra, nested complexes and their nestohedra, and operads and the associahedron diagonal.
Funder
Agence Nationale de la Recherche
Agencia Estatal de Investigación
Banco Santander
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference231 articles.
1. Aguiar, M., Ardila, F.: Hopf Monoids and Generalized Permutahedra. Memoirs of the American Mathematical Society, Vol. 289, No. 1437 (2023)
2. Aneesh, P.B., Banerjee, P., Jagadale, M., John, R.R., Laddha, A., Mahato, S.: On positive geometries of quartic interactions: Stokes polytopes, lower forms on associahedra and world-sheet forms. J. High Energy Phys. 2020(4), Art No. 149 (2020)
3. Ardila, F., Doker, J.: Lifted generalized permutahedra and composition polynomials. Adv. Appl. Math. 50(4), 607–633 (2013)
4. Arkani-Hamed, N., Bai, Y., He, S., Yan, G.: Scattering forms and the positive geometry of kinematics, color and the worldsheet. J. High Energy Phys. 2018(5), Art No. 96 (2018)
5. Aoki, T., Higashitani, A., Iyama, O., Kase, R., Mizuno, Y.: Fans and polytopes in tilting theory I: Foundations. arXiv:2203.15213 (2022)