Eulerian polynomials via the Weyl algebra action
Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook num...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Agapito, Jose [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of algebraic combinatorics - Springer US, 1992, 54(2020), 2 vom: 02. Dez., Seite 457-473 |
|---|---|
| Übergeordnetes Werk: |
volume:54 ; year:2020 ; number:2 ; day:02 ; month:12 ; pages:457-473 |
| Links: |
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| DOI / URN: |
10.1007/s10801-020-00997-6 |
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| 520 | |a Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a Young diagram by replacing the geometric series with the exponential series. Also, by replacing the derivative operator with the q-derivative operator, we extend these results to the q-analogue setting including the q-hit numbers. Finally, a combinatorial description and a proof of the symmetry of a family of polynomials introduced by one of the authors are provided. | ||
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10.1007/s10801-020-00997-6 doi (DE-627)OLC2077131209 (DE-He213)s10801-020-00997-6-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Agapito, Jose verfasserin aut Eulerian polynomials via the Weyl algebra action 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a Young diagram by replacing the geometric series with the exponential series. Also, by replacing the derivative operator with the q-derivative operator, we extend these results to the q-analogue setting including the q-hit numbers. Finally, a combinatorial description and a proof of the symmetry of a family of polynomials introduced by one of the authors are provided. Eulerian polynomials Weyl algebra Rook numbers Permutation statistics Formal power series Petrullo, Pasquale (orcid)0000-0002-8155-7876 aut Senato, Domenico aut Torres, Maria M. aut Enthalten in Journal of algebraic combinatorics Springer US, 1992 54(2020), 2 vom: 02. Dez., Seite 457-473 (DE-627)131180770 (DE-600)1143271-8 (DE-576)033043701 0925-9899 nnns volume:54 year:2020 number:2 day:02 month:12 pages:457-473 https://doi.org/10.1007/s10801-020-00997-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 54 2020 2 02 12 457-473 |
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Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a Young diagram by replacing the geometric series with the exponential series. Also, by replacing the derivative operator with the q-derivative operator, we extend these results to the q-analogue setting including the q-hit numbers. Finally, a combinatorial description and a proof of the symmetry of a family of polynomials introduced by one of the authors are provided. © The Author(s) 2020 |
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Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a Young diagram by replacing the geometric series with the exponential series. Also, by replacing the derivative operator with the q-derivative operator, we extend these results to the q-analogue setting including the q-hit numbers. Finally, a combinatorial description and a proof of the symmetry of a family of polynomials introduced by one of the authors are provided. © The Author(s) 2020 |
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Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a Young diagram by replacing the geometric series with the exponential series. Also, by replacing the derivative operator with the q-derivative operator, we extend these results to the q-analogue setting including the q-hit numbers. Finally, a combinatorial description and a proof of the symmetry of a family of polynomials introduced by one of the authors are provided. © The Author(s) 2020 |
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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">OLC2077131209</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505140040.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">221220s2020 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10801-020-00997-6</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2077131209</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10801-020-00997-6-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">Agapito, Jose</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Eulerian polynomials via the Weyl algebra action</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</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) 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a Young diagram by replacing the geometric series with the exponential series. Also, by replacing the derivative operator with the q-derivative operator, we extend these results to the q-analogue setting including the q-hit numbers. Finally, a combinatorial description and a proof of the symmetry of a family of polynomials introduced by one of the authors are provided.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Eulerian polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weyl algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rook numbers</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Permutation statistics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Formal power series</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Petrullo, Pasquale</subfield><subfield code="0">(orcid)0000-0002-8155-7876</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Senato, Domenico</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Torres, Maria M.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of algebraic combinatorics</subfield><subfield code="d">Springer US, 1992</subfield><subfield code="g">54(2020), 2 vom: 02. 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