Order theory | Algebraic combinatorics
In mathematics, in the branch of combinatorics, a graded poset is a partially-ordered set (poset) P equipped with a rank function ρ from P to the set N of all natural numbers. ρ must satisfy the following two properties: * The rank function is compatible with the ordering, meaning that for all x and y in the order, if x < y then ρ(x) < ρ(y), and * The rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then ρ(y) = ρ(x) + 1. The value of the rank function for an element of the poset is called its rank. Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see Ranked poset. A rank or rank level of a graded poset is the subset of all the elements of the poset that have a given rank value. Graded posets play an important role in combinatorics and can be visualized by means of a Hasse diagram. (Wikipedia).
Determine the values of two angles that lie on a lie with a third angle
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
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)
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
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
How to label triangles depending on the length of their sides
👉 Learn all about classifying triangles. A triangle is a closed figure with three sides. A triangle can be classified based on the length of the sides or based on the measure of the angles. To classify a triangle based on the length of the sides, we have: equilateral (3 sides are equal), i
From playlist Triangles
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
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
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
Partial orders, maxels and Mobius functions | MathFoundations272 | N J Wildberger
This more advanced lecture connects the Boole-Mobius transform between Boolean functions and Boole polynumbers, which is a key tool in understanding circuit analysis from the point of view of the Algebra of Boole. We include a brief discussion of Mobius functions on partially ordered sets
From playlist Boole's Logic and Circuit Analysis
David Meyer (1/30/18): Some algebraic stability theorems for generalized persistence modules
From an algebraic point of view, generalized persistence modules can be interpreted as finitely-generated modules for a poset algebra. We prove an algebraic analogue of the isometry theorem of Bauer and Lesnick for a large class of posets. This theorem shows that for such posets, the int
From playlist AATRN 2018
How to label the sides of an angle
Learn all about angles. An angle is a figure formed by two rays sharing a common endpoint. An angle can be classified as acute, right, obtuse, straight or refrex. An acute angle is an angle which measures less than 90 degrees. A right angle measures 90 degrees. An obtuse angle measures mor
From playlist Learn all about basics of Angles #Geometry
Zorn's Lemma, The Well-Ordering Theorem, and Undefinability (Version 2.0)
Zorn's Lemma and The Well-ordering Theorem are seemingly straightforward statements, but they give incredibly mind-bending results. Orderings, Hasse Diagrams, and the Ordinals / set theory will come up in this video as tools to get a better view of where the "proof" of Zorn's lemma comes f
From playlist The New CHALKboard
Determining two angles that are supplementary
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
From playlist Angle Relationships From a Figure
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
What is an equilateral triangle
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Imaginary Erdős Number - Numberphile
Ron Graham on imaginary Erdős Numbers. More Ron Graham Videos: http://bit.ly/Ron_Graham More links & stuff in full description below ↓↓↓ Numberphile merch: https://www.numberphile.com/merchandise Calculate Erdős Numbers (and collaboration distance) here: http://www.ams.org/mathscinet/coll
From playlist Ron Graham on Numberphile