A Bijective Proof of a Factorization Formula for Specialized Macdonald Polynomials
Abstract Let μ and ν = (ν1, . . . , νk) be partitions such that μ is obtained from ν by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials $${{\tilde{H}_\mu}(X; q, t)}$$ satisfy the identity $${{\tilde{H}_\mu} = \tilde{H}_\nu \tilde{H}_{(r^m)}...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Loehr, Nicholas A. [verfasserIn] |
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Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Anmerkung: |
© Springer Basel 2012 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of combinatorics - SP Birkhäuser Verlag Basel, 1997, 16(2012), 4 vom: 05. Okt., Seite 815-828 |
|---|---|
| Übergeordnetes Werk: |
volume:16 ; year:2012 ; number:4 ; day:05 ; month:10 ; pages:815-828 |
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| DOI / URN: |
10.1007/s00026-012-0162-5 |
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OLC2061534309 |
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| 520 | |a Abstract Let μ and ν = (ν1, . . . , νk) be partitions such that μ is obtained from ν by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials $${{\tilde{H}_\mu}(X; q, t)}$$ satisfy the identity $${{\tilde{H}_\mu} = \tilde{H}_\nu \tilde{H}_{(r^m)}}$$ when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ νk and $${r \in \{1, 2\}}$$ . This note gives a bijective proof of the formula for all r ≤ νk. | ||
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10.1007/s00026-012-0162-5 doi (DE-627)OLC2061534309 (DE-He213)s00026-012-0162-5-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Loehr, Nicholas A. verfasserin aut A Bijective Proof of a Factorization Formula for Specialized Macdonald Polynomials 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Basel 2012 Abstract Let μ and ν = (ν1, . . . , νk) be partitions such that μ is obtained from ν by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials $${{\tilde{H}_\mu}(X; q, t)}$$ satisfy the identity $${{\tilde{H}_\mu} = \tilde{H}_\nu \tilde{H}_{(r^m)}}$$ when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ νk and $${r \in \{1, 2\}}$$ . This note gives a bijective proof of the formula for all r ≤ νk. Niese, Elizabeth aut Enthalten in Annals of combinatorics SP Birkhäuser Verlag Basel, 1997 16(2012), 4 vom: 05. Okt., Seite 815-828 (DE-627)234146176 (DE-600)1394631-6 (DE-576)094078408 0218-0006 nnns volume:16 year:2012 number:4 day:05 month:10 pages:815-828 https://doi.org/10.1007/s00026-012-0162-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2088 GBV_ILN_4277 AR 16 2012 4 05 10 815-828 |
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Abstract Let μ and ν = (ν1, . . . , νk) be partitions such that μ is obtained from ν by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials $${{\tilde{H}_\mu}(X; q, t)}$$ satisfy the identity $${{\tilde{H}_\mu} = \tilde{H}_\nu \tilde{H}_{(r^m)}}$$ when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ νk and $${r \in \{1, 2\}}$$ . This note gives a bijective proof of the formula for all r ≤ νk. © Springer Basel 2012 |
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Abstract Let μ and ν = (ν1, . . . , νk) be partitions such that μ is obtained from ν by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials $${{\tilde{H}_\mu}(X; q, t)}$$ satisfy the identity $${{\tilde{H}_\mu} = \tilde{H}_\nu \tilde{H}_{(r^m)}}$$ when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ νk and $${r \in \{1, 2\}}$$ . This note gives a bijective proof of the formula for all r ≤ νk. © Springer Basel 2012 |
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Abstract Let μ and ν = (ν1, . . . , νk) be partitions such that μ is obtained from ν by adding m parts of size r. Descouens and Morita proved algebraically that the modified Macdonald polynomials $${{\tilde{H}_\mu}(X; q, t)}$$ satisfy the identity $${{\tilde{H}_\mu} = \tilde{H}_\nu \tilde{H}_{(r^m)}}$$ when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ νk and $${r \in \{1, 2\}}$$ . This note gives a bijective proof of the formula for all r ≤ νk. © Springer Basel 2012 |
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Descouens and Morita proved algebraically that the modified Macdonald polynomials $${{\tilde{H}_\mu}(X; q, t)}$$ satisfy the identity $${{\tilde{H}_\mu} = \tilde{H}_\nu \tilde{H}_{(r^m)}}$$ when the parameter t is specialize to an mth root of unity. Descouens, Morita, and Numata proved this formula bijectively when r ≤ νk and $${r \in \{1, 2\}}$$ . This note gives a bijective proof of the formula for all r ≤ νk.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Niese, Elizabeth</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Annals of combinatorics</subfield><subfield code="d">SP Birkhäuser Verlag Basel, 1997</subfield><subfield code="g">16(2012), 4 vom: 05. 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