In mathematics, a ranked partially ordered set or ranked poset may be either: * a graded poset, or * a poset with the property that for every element x, all maximal chains among those with x as greatest element have the same finite length, or * a poset in which all maximal chains have the same finite length. The second definition differs from the first in that it requires all minimal elements to have the same rank; for posets with a least element, however, the two requirements are equivalent. The third definition is even more strict in that it excludes posets with infinite chains and also requires all maximal elements to have the same rank. Richard P. Stanley defines a graded poset of length n as one in which all maximal chains have length n. (Wikipedia).
Art Quiz #107 - American Abstract Expressionism,
From playlist Art Quizzes
Lec 11 | MIT 6.042J Mathematics for Computer Science, Fall 2010
Lecture 11: Relations, Partial Orders, and Scheduling Instructor: Marten van Dijk View the complete course: http://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.042J Mathematics for Computer Science, Fall 2010
Singular Hodge Theory for Combinatorial Geometries by Jacob Matherne
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Steve Oudot (9/8/21): Signed barcodes for multi-parameter persistence via rank decompositions
In this talk I will introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of a poset representation. Like its unsigned counterpart in one-parameter persistence, the signed barcode
From playlist AATRN 2021
Toric Arrangements - Margaret Readdy
Margaret Readdy University of Kentucky; Member, School of Mathematics October 26, 2010 The cd-index is a noncommutative polynomial which compactly encodes the flag vector data of a polytope, and more generally, of a regular cell complex. Ehrenborg and Readdy discovered the cd-index has an
From playlist Mathematics
Martina Lanini: Totally nonnegative Grassmannians, Grassmann necklaces and quiver Grassmannians
30 September 2021 Abstract: Totally nonnegative (tnn) Grassmannians are subvarieties of (real) Grassmannians which have been widely investigated thanks to the several applications in mathematics and physics. In a seminal paper on the subject, Postnikov constructed a cellularisation of the
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Neutrinos and the 2015 Nobel Prize in Physics - Sixty Symbols
The 2015 Nobel Prize in Physics goes to Takaaki Kajita and Arthur B. McDonald for showing that Neutrinos have mass. More Nobel winners: http://bit.ly/SSNobel This video features Ed Copeland, Michael Merrifield and Meghan Gray. More Neutrino videos: https://www.youtube.com/playlist?list=
From playlist Nobel Prize Videos - Sixty Symbols
Ulysses Alvarez - The Up Topology on the Grassmann Poset
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Ulysses Alvarez, Binghamton University Title: The Up Topology on the Grassmann Poset Abstract: For a discrete poset X, McCord proved that there exists a weak homotopy equivalence from the order complex |X| to where X has
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Ana Romero: Effective computation of spectral systems and relation with multi-parameter persistence
Title: Effective computation of spectral systems and their relation with multi-parameter persistence Abstract: Spectral systems are a useful tool in Computational Algebraic Topology that provide topological information on spaces with generalized filtrations over a poset and generalize the
From playlist AATRN 2022
Kolja Knauer : Posets, polynômes, et polytopes - Partie 1
Résumé : Les posets (ensembles partiellement ordonnés) sont des structures utiles pour la modélisation de divers problèmes (scheduling, sous-groupes d'un groupe), mais ils sont aussi la base d'une théorie combinatoire très riche. Nous discuterons des paramètres de posets comme la largeur,
From playlist Combinatorics
Kolja Knauer : Posets, polynômes, et polytopes - Partie 2
Résumé : Les posets (ensembles partiellement ordonnés) sont des structures utiles pour la modélisation de divers problèmes (scheduling, sous-groupes d'un groupe), mais ils sont aussi la base d'une théorie combinatoire très riche. Nous discuterons des paramètres de posets comme la largeur,
From playlist Combinatorics
Fedor Petrov: "Inequalities for posets"
Asymptotic Algebraic Combinatorics 2020 "Inequalities for posets" Fedor Petrov - Steklov Institute of Mathematics at St. Petersburg Abstract: We discuss several recent inequalities between combinatorial characteristics of posets: hooks and antihooks, chains and antichains, number of line
From playlist Asymptotic Algebraic Combinatorics 2020