Spectrahedrality of hyperbolicity cones of multivariate matching polynomials
Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate ve...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Amini, Nima [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2018 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of algebraic combinatorics - Springer US, 1992, 50(2018), 2 vom: 16. Okt., Seite 165-190 |
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| Übergeordnetes Werk: |
volume:50 ; year:2018 ; number:2 ; day:16 ; month:10 ; pages:165-190 |
| Links: |
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| DOI / URN: |
10.1007/s10801-018-0848-9 |
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OLC2034254341 |
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| 520 | |a Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman. | ||
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| 650 | 4 | |a Hyperbolic polynomial | |
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| 650 | 4 | |a Multivariate matching polynomial | |
| 650 | 4 | |a Multivariate independence polynomial | |
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10.1007/s10801-018-0848-9 doi (DE-627)OLC2034254341 (DE-He213)s10801-018-0848-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Amini, Nima verfasserin (orcid)0000-0002-2305-9764 aut Spectrahedrality of hyperbolicity cones of multivariate matching polynomials 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman. Generalized Lax conjecture Hyperbolic polynomial Stable polynomial Multivariate matching polynomial Multivariate independence polynomial Enthalten in Journal of algebraic combinatorics Springer US, 1992 50(2018), 2 vom: 16. Okt., Seite 165-190 (DE-627)131180770 (DE-600)1143271-8 (DE-576)033043701 0925-9899 nnns volume:50 year:2018 number:2 day:16 month:10 pages:165-190 https://doi.org/10.1007/s10801-018-0848-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4323 AR 50 2018 2 16 10 165-190 |
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10.1007/s10801-018-0848-9 doi (DE-627)OLC2034254341 (DE-He213)s10801-018-0848-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Amini, Nima verfasserin (orcid)0000-0002-2305-9764 aut Spectrahedrality of hyperbolicity cones of multivariate matching polynomials 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman. Generalized Lax conjecture Hyperbolic polynomial Stable polynomial Multivariate matching polynomial Multivariate independence polynomial Enthalten in Journal of algebraic combinatorics Springer US, 1992 50(2018), 2 vom: 16. Okt., Seite 165-190 (DE-627)131180770 (DE-600)1143271-8 (DE-576)033043701 0925-9899 nnns volume:50 year:2018 number:2 day:16 month:10 pages:165-190 https://doi.org/10.1007/s10801-018-0848-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4323 AR 50 2018 2 16 10 165-190 |
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10.1007/s10801-018-0848-9 doi (DE-627)OLC2034254341 (DE-He213)s10801-018-0848-9-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Amini, Nima verfasserin (orcid)0000-0002-2305-9764 aut Spectrahedrality of hyperbolicity cones of multivariate matching polynomials 2018 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2018 Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman. Generalized Lax conjecture Hyperbolic polynomial Stable polynomial Multivariate matching polynomial Multivariate independence polynomial Enthalten in Journal of algebraic combinatorics Springer US, 1992 50(2018), 2 vom: 16. Okt., Seite 165-190 (DE-627)131180770 (DE-600)1143271-8 (DE-576)033043701 0925-9899 nnns volume:50 year:2018 number:2 day:16 month:10 pages:165-190 https://doi.org/10.1007/s10801-018-0848-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4323 AR 50 2018 2 16 10 165-190 |
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Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman. © The Author(s) 2018 |
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Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman. © The Author(s) 2018 |
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Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally, we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman. © The Author(s) 2018 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2034254341</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503103005.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2018 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10801-018-0848-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2034254341</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10801-018-0848-9-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Amini, Nima</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-2305-9764</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Spectrahedrality of hyperbolicity cones of multivariate matching polynomials</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2018</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2018</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application, we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). 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