Infinite graphs | Integer sequences
In crystallography and the theory of infinite vertex-transitive graphs, the coordination sequence of a vertex is an integer sequence that counts how many vertices are at each possible distance from . That is, it is a sequence where each is the number of vertices that are steps away from . If the graph is vertex-transitive, then the sequence is an invariant of the graph that does not depend on the specific choice of . Coordination sequences can also be defined for sphere packings, by using either the contact graph of the spheres or the Delaunay triangulation of their centers, but these two choices may give rise to different sequences. As an example, in a square grid, for each positive integer , there are grid points that are steps away from the origin. Therefore, the coordination sequence of the square grid is the sequence in which, except for the initial value of one, each number is a multiple of four. The concept was proposed by Georg O. Brunner and Fritz Laves and later developed by Michael O'Keefe. The coordination sequences of many low-dimensional lattices and uniform tilings are known. (Wikipedia).
What is the definition of a geometric sequence
๐ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the alternate in sign sequence
๐ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
This video introduces geometric sequences. http://mathispower4u.yolasite.com/
From playlist Infinite Series
What is the definition of an arithmetic sequence
๐ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
๐ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is an arithmetic sequence
๐ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Learn to write the explicit formula for the geometric sequence
๐ Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi
From playlist Sequences
How to write the explicit formula of a geometric sequence given two terms of
๐ Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi
From playlist Sequences
What are the formulas for arithmetic and geometric sequences
๐ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Norm Form Equations and Linear Divisibility Sequences (CTNT 2020)
Contact Information: Elisa Bellah ebellah@uoregon.edu pages.uoregon.edu/ebellah Abstract: Finding integer solutions to norm form equations is a classic Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It tur
From playlist CTNT 2020 - Conference Videos
Dima Grigoriev, University of Lille
March 19, Dima Grigoriev, University of Lille Tropical recurrent sequences
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Giray รkten: Number sequences for simulation - lecture 2
After an overview of some approaches to define random sequences, we will discuss pseudorandom sequences and low-discrepancy sequences. Applications to numerical integration, Koksma-Hlawka inequality, and Niederreiterโs uniform point sets will be discussed. We will then present randomized q
From playlist Probability and Statistics
A Non-flag Arithmetic Regularity Lemma and Counting Lemma - Daniel Altman
Special Year Informal Seminar Topic: A Non-flag Arithmetic Regularity Lemma and Counting Lemma Speaker: Daniel Altman Affiliation: University of Oxford Date: March 10, 2023 We will discuss a version of the Green--Tao arithmetic regularity lemma and counting lemma which works in the gener
From playlist Mathematics
Lyapunov's Fractal (that Lyapunov knew nothing about) #SoME2
Hi everyone! I hope you enjoy my first video. I've known about Markus-Lyapunov Fractals for a few years now, and it surprised me that I couldn't find any video explaining how they work - so I thought I'd take a stab at it myself! This is also my submission for Summer of Math Exposition 2.
From playlist Summer of Math Exposition 2 videos
Metric Spaces - Lectures 17 & 18: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 9th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Stable Homotopy Seminar, 10: Fiber and Cofiber Sequences of Spectra
(Note: some internet issues forced me to do the second half of this on the blackboard, so the quality's a bit worse.) We generalize the notion of fiber & cofiber sequence to arbitrary pointed model categories, using the notion of homotopy limit and colimit defined last time. Cofiber sequ
From playlist Stable Homotopy Seminar
Simon Brain: The Gysin Sequence for Quantum Lens Spaces
This is a joint with Francesca Arici and Giovanni Landi. We construct an analogue of the Gysin sequence for circle bundles, now for q-deformed lens spaces in the sense of Vaksman-Soibelman. Our proof that the sequence is exact relies heavily on the non commutative APS index theory of Care
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Trevor Martin, Coordinated evolution of gene expression across 309 marine microbial species
On March 1, 2016, Mr. Martin delivered this talk at the annual CEHG symposium on Stanford campus. CEHG is Stanford's Center for Computational, Evolutionary and Human Genomics.
From playlist Stanford CEHG Speaker Playlist
How to write the explicit formula for a geometric sequence given the 10th term and ratio
๐ Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi
From playlist Sequences
Algorithmic Stochastic Localization for the Sherrington-Kirkpatrick Model - Mark Sellke
Computer Science/Discrete Mathematics Seminar I Topic: Algorithmic Stochastic Localization for the Sherrington-Kirkpatrick Model Speaker: Mark Sellke Affiliation: Member, School of Mathematics Date: November 28, 2022ย Sampling from high-dimensional, multimodal distributions is a computat
From playlist Mathematics