Descent polynomials
Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a descr...
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| Autor*in: |
Diaz-Lopez, Alexander [verfasserIn] |
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E-Artikel |
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Englisch |
| Erschienen: |
2019transfer abstract |
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| Umfang: |
13 |
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| Übergeordnetes Werk: |
Enthalten in: A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations - Guo, Bangwei ELSEVIER, 2023, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:342 ; year:2019 ; number:6 ; pages:1674-1686 ; extent:13 |
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| DOI / URN: |
10.1016/j.disc.2019.01.034 |
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ELV046399968 |
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| 520 | |a Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. | ||
| 520 | |a Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. | ||
| 650 | 7 | |a Descent polynomial |2 Elsevier | |
| 650 | 7 | |a Descent set |2 Elsevier | |
| 650 | 7 | |a Roots |2 Elsevier | |
| 650 | 7 | |a Coefficients |2 Elsevier | |
| 650 | 7 | |a Coxeter group |2 Elsevier | |
| 650 | 7 | |a Consecutive pattern avoidance |2 Elsevier | |
| 700 | 1 | |a Harris, Pamela E. |4 oth | |
| 700 | 1 | |a Insko, Erik |4 oth | |
| 700 | 1 | |a Omar, Mohamed |4 oth | |
| 700 | 1 | |a Sagan, Bruce E. |4 oth | |
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10.1016/j.disc.2019.01.034 doi GBV00000000000581.pica (DE-627)ELV046399968 (ELSEVIER)S0012-365X(19)30045-7 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Diaz-Lopez, Alexander verfasserin aut Descent polynomials 2019transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. Descent polynomial Elsevier Descent set Elsevier Roots Elsevier Coefficients Elsevier Coxeter group Elsevier Consecutive pattern avoidance Elsevier Harris, Pamela E. oth Insko, Erik oth Omar, Mohamed oth Sagan, Bruce E. oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:6 pages:1674-1686 extent:13 https://doi.org/10.1016/j.disc.2019.01.034 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 6 1674-1686 13 |
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10.1016/j.disc.2019.01.034 doi GBV00000000000581.pica (DE-627)ELV046399968 (ELSEVIER)S0012-365X(19)30045-7 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Diaz-Lopez, Alexander verfasserin aut Descent polynomials 2019transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. Descent polynomial Elsevier Descent set Elsevier Roots Elsevier Coefficients Elsevier Coxeter group Elsevier Consecutive pattern avoidance Elsevier Harris, Pamela E. oth Insko, Erik oth Omar, Mohamed oth Sagan, Bruce E. oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:6 pages:1674-1686 extent:13 https://doi.org/10.1016/j.disc.2019.01.034 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 6 1674-1686 13 |
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10.1016/j.disc.2019.01.034 doi GBV00000000000581.pica (DE-627)ELV046399968 (ELSEVIER)S0012-365X(19)30045-7 DE-627 ger DE-627 rakwb eng 610 VZ 44.64 bkl 44.32 bkl Diaz-Lopez, Alexander verfasserin aut Descent polynomials 2019transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. Descent polynomial Elsevier Descent set Elsevier Roots Elsevier Coefficients Elsevier Coxeter group Elsevier Consecutive pattern avoidance Elsevier Harris, Pamela E. oth Insko, Erik oth Omar, Mohamed oth Sagan, Bruce E. oth Enthalten in Elsevier Guo, Bangwei ELSEVIER A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations 2023 Amsterdam [u.a.] (DE-627)ELV009312048 volume:342 year:2019 number:6 pages:1674-1686 extent:13 https://doi.org/10.1016/j.disc.2019.01.034 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 44.64 Radiologie VZ 44.32 Medizinische Mathematik medizinische Statistik VZ AR 342 2019 6 1674-1686 13 |
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610 VZ 44.64 bkl 44.32 bkl Descent polynomials Descent polynomial Elsevier Descent set Elsevier Roots Elsevier Coefficients Elsevier Coxeter group Elsevier Consecutive pattern avoidance Elsevier |
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A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations |
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A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations |
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Descent polynomials |
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Diaz-Lopez, Alexander |
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A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations |
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A robust and lightweight deep attention multiple instance learning algorithm for predicting genetic alterations |
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10.1016/j.disc.2019.01.034 |
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descent polynomials |
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Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. |
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Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. |
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Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n . We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout. |
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Harris, Pamela E. Insko, Erik Omar, Mohamed Sagan, Bruce E. |
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