This is one of my first illustrations for the Seymour Second Neighborhood Conjecture #SSNC. It's an oriented graph. I noticed patterns, number of nodes in each neighborhood. #MathIsBeautiful 1->7 2->6 3->5 Second, number of cycles. 1->1 2->2 3->2 (can't have 3) alphaxiv.org/abs/2501.00614

This is an oriented graph for the Seymour Second Neighborhood Conjecture #SSNC. Nodes are in "rooted neighborhoods". We see patterns, number of nodes in each neighborhood. #MathIsBeautiful 1->7 2->6 3->5 Second, number of cycles. 1->1 2->2 3->2 (can't have 3) alphaxiv.org/abs/2501.00614

I'm excited to share my #Math paper, alphaxiv.org/abs/2501.00614 It is my constructive #ProofByContradicton of the Seymour Second Neighborhood Conjecture, using #DataStructures and #Algorithms, #BFS and #coding intuition and rigor to #Research this #OpenProblem in #GraphTheory.

I'm excited to share my #Math paper, alphaxiv.org/abs/2501.00614 It is my constructive #ProofByContradicton of the Seymour Second Neighborhood Conjecture, using #DataStructures and #Algorithms, #BFS and #coding intuition and rigor to #Research this #OpenProblem in #GraphTheory.

I'm excited to share my latest #Math paper, alphaxiv.org/abs/2501.00614 It is my constructive #ProofByContradicton of the Seymour Second Neighborhood Conjecture, using #DataStructures and #Algorithms, #BFS and #coding intuition and rigor to solve this #OpenProblem in #GraphTheory.

I'm excited to share my latest #Math paper, alphaxiv.org/abs/2501.00614 It is my constructive #ProofByContradicton of the Seymour Second Neighborhood Conjecture, using #DataStructures and #Algorithms, #BFS and #coding intuition and rigor to solve this #OpenProblem in #GraphTheory.

I'm excited to share my latest #Math paper, alphaxiv.org/abs/2501.00614 It is my constructive #ProofByContradicton of the Seymour Second Neighborhood Conjecture, using #DataStructures and #Algorithms, #BFS and #coding intuition and rigor to solve this #OpenProblem in #GraphTheory.

I'm excited to share my latest #Math paper, alphaxiv.org/abs/2501.00614 It is my constructive #ProofByContradicton of the Seymour Second Neighborhood Conjecture, using #DataStructures and #Algorithms, #BFS and #coding intuition and rigor to solve this #OpenProblem in #GraphTheory.

My Biblical thought of the day, Jesus went through Samaria, a town that Jews would walk mikes to avoid. So after the Resurrection, did this continue? Did Christians like Paul continue looking for converts in Sameria?

As a person with ADHD I thought Pinterest would be the thing that saved my life because I could put all those screenshots somewhere. But it's so confusing.

Who bears the brunt of these cuts? Well, here's a word cloud of the most frequent terms from the titles and abstracts of terminated grants, with word size proportional to frequency:

UPDATE: We have data on >1000 terminated #NSF grants at grant-watch.us. Thanks to all who have been contributing data the past few days. We've also added a "Reports" section with some analyses. For NSF, we see that the STEM education directorate has been absolutely pummeled.

Men kidnapped by the Trump regime spell out an SOS at the Bluebonnet ICE concentration camp.

A Pacers fan brought a free throw clock for Giannis 😂

"He don't need no music!" Remembering Luther Vandross on his birthday 🕊️💙 (April 20, 1951 – July 1, 2005)

I want to add #PrincessBride quotes to a talk I'm giving. People are saying I shouldn't because the kids won't know the movie. I'm saying they should learn it. It's that important. Who's right? (It's me)

Why does adding a tip feel like taking an SAT

I'm reading I Samuel and now I have the question, what does it mean when the Lord repents?

They say math is woke

Did he just threaten the Supreme Court

#ArtistFave15 #MusicChallenge 2) No Ordinary Love The seven minute lead single from Love Deluxe that feels like it should go on forever. youtu.be/au8rHGvytn8?...

Day 20 of #SSNC facts! We're examining how standard #algorithms handle the #SeymourConjecture's. Remember, this #Conjecture seeks an #OrientedGraph whose second neighborhood is at least as large as its first. We last looked at Dijkstra. Today, Bellman-Ford. #ComputerScience #Math

Day 19 of #SSNC facts! We're exploring why the #SeymourConjecture remains unsolved. Today, we examine how #algorithms like #Dijkstra #Algorithm handle the challenge of neighborhood analysis. #math #mathematics #compSci #computerScience

Day 18 of #SSNC facts! We're looking at the #SeymourConjecture: Does every #OrientedGraph have a node with a second neighborhood at least as large as its first? Can traditional #GraphTheory #Algorithms solve the neighborhood size challenge? Today, we examine #DepthFirstSearch (DFS). #Math

How a problem about pigeons powers complexity theory

Day 17 of #SSNC facts! Remember, we're exploring: Does every #OrientedGraph have a node with a second neighborhood at least as large as its first? Why is this deceptively simple question still unsolved? #GraphTheory #Resesrch #Math #ComputerScience #SeymourConjecture

Day 16 of #SSNC facts! We've been discussing the #SeymourConjecture: It asks the questionv Does every #OrientedGraph have a node whose second neighborhood is at least as large as its first? Open since 1990, but why is this still unsolved? Let's explore. #GraphTheory #Math #ComputerScience

Day 15 of #SSNC facts. Remember, for a Constraint Satisfaction Problem, we're not looking for a solution, but proving there ISN'T one. If a CSP is 'unsatisfiable', it means certain scenarios that break the #SSNC are impossible, improving our bounds! #MathLogic #Bounds #SeymourConjecture

:: BREAKING NOW: Multiple polling places across Milwaukee are running low or have run out of ballots as turnout is at record levels. MKE Election Commission is aware and sending out fresh ballots. If you are in line -- or know someone who is -- ballots are on the way.

Day 14 of #SSNC facts! We're diving into Constraint Satisfaction Problems (CSPs). Let's talk about how they are used to tackle the #SeymourConjecture. Think of CSPs as a set of rules we ask a computer to try and solve. #GraphTheory #CSP #math

Day 13 of #SSNC facts! Did you know #DominatingSets are relevant to the #SeymourConjecture? A dominating set is a vertex subset where every other vertex is adjacent to one in the set. How might this relate to neighborhoods? #GraphTheory #SSNC #math #compsci #ComputerScience

Day 12 of #SSNC facts! Fisher: Existence proof (probabilistic). Thomassé: Constructive proof (median orders). Both solved Dean's Conjecture, but Thomassé provided a path to #algorithms. This was a fundamental shift in approach! #MathematicalProofs #AlgorithmDesign #GraphTheory #SeymourConjecture

We're planning a 2-day "Celebration of Theoretical Computer Science" mentoring workshop on Dec 11-12, ahead of #FOCS2025, as a satellite event held at U Sydney. Focusing on the diversity of people and thought in TCS, and the incredible advances it enabled and will continue to enable. Stay tuned!

Day 11 of #SSNC facts! Let's explore Thomassé's (w/ Havet) approach to the #DeanConjecture! They introduced "median orders" in tournaments. This is as a way to arrange vertices to reveal structural properties. This is a powerful combinatorial tool! #GraphTheory #MedianOrders #Combinatorics #math

🚨 BREAKING: Long COVID research grants rescinded earlier this week have been restored, according to researchers & patient reps. Advocates organized quickly yesterday in response to the news, helping reverse the decision. Exclusive in @thesicktimes.bsky.social thesicktimes.org/2025/03/28/u...

Day 10 of #SSNC facts! The #DeanConjecture states in any tournament, there's a vertex 'v' where |out-neighborhood(v, 2)| ≥ |out-neighborhood(v, 1)|. Simply put, you can reach more vertices in 2 steps than 1. Fisher provided a probabilistic proof. #GraphTheory #SeymourConjecture #math #research

This is a great article on the history of arxiv @teakayb.mathsy.space @fortnow.bsky.social

Modern science wouldn’t exist without the online research repository known as arXiv. Three decades in, its creator still can’t let it go.

My first paper on arxiv is more than 30 years ago. Thank you, arxiv, for existing.

Day 9 of #SSNC facts! Let's explore #tournaments. These are complete #OrientedGraphs. Every node pair has exactly one directed edge. The #DeanLatkaConjecture asks: is there always a node with a second neighborhood at least as large as its first? #GraphTheory #Math #research

Day 8 of SSNC facts! Yesterday we mentioned that the #SeymourConjecture isn't alone. Lets look at the #SullivanConjecture. It asks if the out-degrees of a node's second out-neighborhood are at least twice its in-degree. How are these conjectures similar? Different? #GraphTheory #OpenProblems #math

A Year of Comments on arXiv Papers: Early Lessons from alphaXiv #math #mathematics #compsci #computerscience #graphtheory #datascience #dev #algorithms

The opening from AntZ where he talks about his place in life and says "otherwise I'll just curl up on a larval position and weep! The whole system makes me feel ... Insignificant!" And the psych responds "Yes. Z. You are insignificant"

"Competition". People are told to complete for "1st place" in one metric not there are infinite other metrics they can shine in. Just do you. Society is not public school any more.

I gamify almost beverything.

Humility. Most powerful is a strong concept, but I learned that I'm not invincible.

Empathy. Maybe it's a part of love, but maybe it's not. There's something special about being able to relate to someone and feel their pain.