Timeline for How to recognise that the polynomial method might work
Current License: CC BY-SA 2.5
7 events
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| May 10, 2015 at 22:47 | comment | added | Anurag | @Seva: There is a multiplicity version of Combinatorial Nullstellensatz as well. See Theorem 3.1 in S. Ball and O. Serra, Punctured Combinatorial Nullstellensätze, Combinatorica 29 (2009), 511-522. | |
| Oct 26, 2010 at 8:50 | comment | added | Fedor Petrov | @Seva: OK, but this fact immediately follows from the formula (and from other proofs of CN: we use degree condition exactly for showing that any other monomial has less degree then our in at least one variable.) But I agree that it is worth to state such fact explicitly. | |
| Oct 26, 2010 at 6:57 | comment | added | Seva | @Fedor: for me, the major thing to learn for Lason's paper is not the formula, but the fact that the assumptions of the CN can be slightly relaxed. | |
| Oct 25, 2010 at 21:44 | comment | added | Fedor Petrov | Remark on Lason's paper. As I know (from Noga Alon), formula for coefficient (Theorem 3 in the paper you cite), proving CN, was known before. And in any case, it may be proved much easier, then in this paper. Just note that both LHS and КРЫ are linear in $f$, so we may think that $f$ is monomial. For monomial, everything reduces to dimension 1 (it factors into product over all variables). For dimension 1 it is nothing but Lagrange interpolation. Some applications of it see here lanl.arxiv.org/abs/1005.1177 (I am very sorry for self-advertising). | |
| Oct 25, 2010 at 20:44 | history | edited | Seva | CC BY-SA 2.5 |
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| Oct 25, 2010 at 20:01 | history | edited | Seva | CC BY-SA 2.5 |
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| Oct 25, 2010 at 15:44 | history | answered | Seva | CC BY-SA 2.5 |