Alon’s Nullstellensatz for multisets
Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precis...
Ausführliche Beschreibung
Autor*in: |
Kós, Géza [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2012 |
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Anmerkung: |
© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 |
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Übergeordnetes Werk: |
Enthalten in: Combinatorica - Springer-Verlag, 1981, 32(2012), 5 vom: Mai, Seite 589-605 |
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Übergeordnetes Werk: |
volume:32 ; year:2012 ; number:5 ; month:05 ; pages:589-605 |
Links: |
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DOI / URN: |
10.1007/s00493-012-2758-0 |
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Katalog-ID: |
OLC207387083X |
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520 | |a Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. | ||
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10.1007/s00493-012-2758-0 doi (DE-627)OLC207387083X (DE-He213)s00493-012-2758-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kós, Géza verfasserin aut Alon’s Nullstellensatz for multisets 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. Rónyai, Lajos aut Enthalten in Combinatorica Springer-Verlag, 1981 32(2012), 5 vom: Mai, Seite 589-605 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:32 year:2012 number:5 month:05 pages:589-605 https://doi.org/10.1007/s00493-012-2758-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4323 AR 32 2012 5 05 589-605 |
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10.1007/s00493-012-2758-0 doi (DE-627)OLC207387083X (DE-He213)s00493-012-2758-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kós, Géza verfasserin aut Alon’s Nullstellensatz for multisets 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. Rónyai, Lajos aut Enthalten in Combinatorica Springer-Verlag, 1981 32(2012), 5 vom: Mai, Seite 589-605 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:32 year:2012 number:5 month:05 pages:589-605 https://doi.org/10.1007/s00493-012-2758-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4323 AR 32 2012 5 05 589-605 |
allfields_unstemmed |
10.1007/s00493-012-2758-0 doi (DE-627)OLC207387083X (DE-He213)s00493-012-2758-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kós, Géza verfasserin aut Alon’s Nullstellensatz for multisets 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. Rónyai, Lajos aut Enthalten in Combinatorica Springer-Verlag, 1981 32(2012), 5 vom: Mai, Seite 589-605 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:32 year:2012 number:5 month:05 pages:589-605 https://doi.org/10.1007/s00493-012-2758-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4323 AR 32 2012 5 05 589-605 |
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10.1007/s00493-012-2758-0 doi (DE-627)OLC207387083X (DE-He213)s00493-012-2758-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kós, Géza verfasserin aut Alon’s Nullstellensatz for multisets 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. Rónyai, Lajos aut Enthalten in Combinatorica Springer-Verlag, 1981 32(2012), 5 vom: Mai, Seite 589-605 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:32 year:2012 number:5 month:05 pages:589-605 https://doi.org/10.1007/s00493-012-2758-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4323 AR 32 2012 5 05 589-605 |
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10.1007/s00493-012-2758-0 doi (DE-627)OLC207387083X (DE-He213)s00493-012-2758-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Kós, Géza verfasserin aut Alon’s Nullstellensatz for multisets 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. Rónyai, Lajos aut Enthalten in Combinatorica Springer-Verlag, 1981 32(2012), 5 vom: Mai, Seite 589-605 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:32 year:2012 number:5 month:05 pages:589-605 https://doi.org/10.1007/s00493-012-2758-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_105 GBV_ILN_267 GBV_ILN_2004 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4314 GBV_ILN_4318 GBV_ILN_4323 AR 32 2012 5 05 589-605 |
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alon’s nullstellensatz for multisets |
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Alon’s Nullstellensatz for multisets |
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Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 |
abstractGer |
Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 |
abstract_unstemmed |
Abstract Alon’s combinatorial Nullstellensatz (Theorem 1.1 from [2]) is one of the most powerful algebraic tools in combinatorics, with a diverse array of applications. Let $$\mathbb{F}$$ be a field, S1, S2,..., Sn be finite nonempty subsets of $$\mathbb{F}$$. Alon’s theorem is a specialized, precise version of the Hilbertsche Nullstellensatz for the ideal of all polynomial functions vanishing on the set $$S = S_1 \times S_2 \times \ldots \times S_n \subseteq \mathbb{F}^n$$. From this Alon deduces a simple and amazingly widely applicable nonvanishing criterion (Theorem 1.2 in [2]). It provides a sufficient condition for a polynomial f(x1,..., xn) which guarantees that f is not identically zero on the set S. In this paper we extend these two results from sets of points to multisets. We give two different proofs of the generalized nonvanishing theorem.We extend some of the known applications of the original nonvanishing theorem to a setting allowing multiplicities, including the theorem of Alon and Füredi on the hyperplane coverings of discrete cubes. © János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2012 |
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