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- Physics Related News: Israel Joining CERN, Pugwash and Global Zero, The Replication Crisis, and MAX the Damon.
- Test your intuition 52: Can you predict the ratios of ones?
- Amnon Shashua’s lecture at Reichman University: A Deep Dive into LLMs and their Future Impact.
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- Questions and Concerns About Google’s Quantum Supremacy Claim
- An Aperiodic Monotile
- Test your intuition 52: Can you predict the ratios of ones?
- A Mysterious Duality Relation for 4-dimensional Polytopes.
- TYI 30: Expected number of Dice throws
- The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond
- A Nice Example Related to the Frankl Conjecture
- Quantum Computers: A Brief Assessment of Progress in the Past Decade
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
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Tag Archives: Trees
Lawler-Kozdron-Richards-Stroock’s combined Proof for the Matrix-Tree theorem and Wilson’s Theorem
David Wilson and a cover of Shlomo’s recent book “Curvature in mathematics and physics” A few weeks ago, in David Kazhdan’s basic notion seminar, Shlomo Sternberg gave a lovely presentation Kirchhoff and Wilson via Kozdron and Stroock. The lecture is based on … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Probability
Tagged David Wilson, Gustav Kirchhoff, Trees
4 Comments
A Proof by Induction with a Difficulty
The time has come to prove that the number of edges in every finite tree is one less than the number of vertices (a tree is a connected graph with no cycle). The proof is by induction, but first you need … Continue reading
A Beautiful Garden of Hypertrees
We had a series of posts (1,2,3,4) “from Helly to Cayley” on weighted enumeration of Q-acyclic simplicial complexes. The simplest case beyond Cayley’s theorem were Q-acyclic complexes with vertices, edges, and triangles. One example is the six-vertex triangulation of the … Continue reading
Posted in Combinatorics
Tagged Mishael Rosenthal, Nati Linial, Roy Meshulam, Topological combinatorics, Trees
1 Comment
Helly’s Theorem, “Hypertrees”, and Strange Enumeration I
1. Helly’s theorem and Cayley’s formula Helly’s theorem asserts: For a family of n convex sets in , n > d, if every d+1 sets in the family have a point in common then all members in the family have a point in common. … Continue reading
Posted in Combinatorics, Convexity
Tagged Cayley theorem, Helly Theorem, Simplicial complexes, Topological combinatorics, Trees
10 Comments