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bio website gilkalai.wordpress.com
location Jerusalem
age 59
visits member for 5 years, 10 months
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Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Aug
19
awarded  Favorite Question
Aug
19
comment 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
comment Important formulas in Combinatorics
In short, Asaf, my answer is YES!
Aug
19
answered Important formulas in Combinatorics
Aug
19
comment 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
comment 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
comment 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
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Aug
17
awarded  Nice Question
Aug
17
comment Important formulas in Combinatorics
I would adopt it as a formula in combinatorics any day!
Aug
17
comment 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