bio | website | gilkalai.wordpress.com |
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location | Jerusalem | |
age | 59 | |
visits | member for | 5 years, 10 months |
seen | 20 mins ago | |
stats | profile views | 18,374 |
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University
Aug
19 |
awarded | Favorite Question |
Aug
19 |
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Important formulas in Combinatorics
Here is a post about it (in a simpler form) gilkalai.wordpress.com/2012/01/18/… |
Aug
19 |
awarded | Notable Question |
Aug
19 |
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Important formulas in Combinatorics
In short, Asaf, my answer is YES! |
Aug
19 |
answered | Important formulas in Combinatorics |
Aug
19 |
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Important formulas in Combinatorics
I would represent the matrix tree theorem as: $$\kappa (G) = det (L^-(G)(L^-(G))^{tr}).$$ Here $\kappa (G)$ is the number of spanning trees and $L^-(G)$ is the reduced Laplacian. (The Laplacian with one row deleted). Referring to the determinant rather than eigenvalues is relevant to the proof of the theorem. |
Aug
18 |
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Important formulas in Combinatorics
Dear Darij, This is a formula in combinatorics even in a very strict sense since it applies to Eulerian (d-1)-dimensional simplicial complexes, namely to complexes so that links of faces have the same Euler combinatorics as a sphere of the same dimension. Moreover relations between face numbers of polytopes, and even of complexes described by topological conditions are regarded part of combinatorics. |
Aug
18 |
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Important formulas in Combinatorics
Dear Asaf, as I see it, we want important formulas representing major progress in combinatorics; so infinitary combinatorics applies as well. As I see it: it need to be a formula, it need to be stated explicitly, and it need to be related to important research advances. Maybe we should avoid classic famous very well-known formulas, so I would regard $2^\lambda >\lambda$ as too basic to be included. |
Aug
18 |
answered | Important formulas in Combinatorics |
Aug
18 |
awarded | Good Question |
Aug
18 |
awarded | Popular Question |
Aug
17 |
awarded | Nice Question |
Aug
17 |
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Important formulas in Combinatorics
I would adopt it as a formula in combinatorics any day! |
Aug
17 |
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Important formulas in Combinatorics
This is certainly a great formula! |
Aug
17 |
answered | Important formulas in Combinatorics |
Aug
17 |
asked | Important formulas in Combinatorics |
Aug
11 |
awarded | Necromancer |
Aug
11 |
answered | How is differential geometry used in immediate industrial applications and what are some source to know about it? |
Aug
6 |
answered | Statements reliant on conjectures |
Aug
4 |
awarded | Good Answer |