The descent set polynomial revisited

Richard Ehrenborg; N. Bradley Fox

doi:10.1016/j.ejc.2015.03.027

The descent set polynomial revisited

Richard Ehrenborg, N. Bradley Fox

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We continue to explore cyclotomic factors in the descent set polynomial Q_n(t), which was introduced by Chebikin, Ehrenborg, Pylyavskyy and Readdy. We obtain large classes of factors of the form Φ_2s or Φ_4s where s is an odd integer, with many of these being of the form Φ_2p where p is a prime. We also show that if Φ₂ is a factor of Q_2n(t) then it is a double factor. Finally, we give conditions for an odd prime power q=p^r for which Φ_2p is a double factor of Q_2q(t) and of Q_q+1(t).

Original language	English
Pages (from-to)	47-68
Number of pages	22
Journal	European Journal of Combinatorics
Volume	51
DOIs	https://doi.org/10.1016/j.ejc.2015.03.027
State	Published - Jan 2016

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Publisher Copyright:
© 2015 Elsevier Ltd.

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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title = "The descent set polynomial revisited",

abstract = "We continue to explore cyclotomic factors in the descent set polynomial Qn(t), which was introduced by Chebikin, Ehrenborg, Pylyavskyy and Readdy. We obtain large classes of factors of the form Φ2s or Φ4s where s is an odd integer, with many of these being of the form Φ2p where p is a prime. We also show that if Φ2 is a factor of Q2n(t) then it is a double factor. Finally, we give conditions for an odd prime power q=pr for which Φ2p is a double factor of Q2q(t) and of Qq+1(t).",

author = "Richard Ehrenborg and Fox, {N. Bradley}",

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year = "2016",

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doi = "10.1016/j.ejc.2015.03.027",

language = "English",

volume = "51",

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AU - Fox, N. Bradley

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AB - We continue to explore cyclotomic factors in the descent set polynomial Qn(t), which was introduced by Chebikin, Ehrenborg, Pylyavskyy and Readdy. We obtain large classes of factors of the form Φ2s or Φ4s where s is an odd integer, with many of these being of the form Φ2p where p is a prime. We also show that if Φ2 is a factor of Q2n(t) then it is a double factor. Finally, we give conditions for an odd prime power q=pr for which Φ2p is a double factor of Q2q(t) and of Qq+1(t).

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VL - 51

SP - 47

EP - 68

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

ER -

The descent set polynomial revisited

Abstract

Bibliographical note

ASJC Scopus subject areas

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