04-12-2024
The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Algebra and Logic with the title: “The stylic monoid (and other power quotients)”. Antoine Abram (Université du Québec à Montréal) is the speaker.
Abstract: The plactic monoid is a central object in algebraic combinatorics. Generally represented with Young tableaux, Cain, Gray and Malheiro proved that it has a confluent presentation with column tableaux as generators. We will look at a left action of the free monoid A* on this set of generators by Schensted left insertion. This action defines a monoid, called the stylic monoid, which happens to be a non-trivial finite quotient of the plactic monoid. It has a nice presentation by simply quotienting the plactic monoid by the relations x2 = x for all letters x in A. We will look at some interesting properties using a set of representants, the N-tableaux, paired with insertion algorithms.
If time permits, we will conclude with some generalization and analogous quotients called power quotients.
Based on joint work with C. Reutenauer for the stylic monoid, and with F. Hivert, J. Mitchell, M. Tsalakou, and J.-C. Novelli for the power quotients.
Zoom link: https://videoconf-colibri.zoom.us/j/97149261405?pwd=dwPsbvzqf72uSGBWpW0Y...
Monday, 9 December 2024, from 14:00 to 15:00.