Timeline for Cyclotomic polynomials in combinatorics
Current License: CC BY-SA 4.0
29 events
| when toggle format | what | by | license | comment | |
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| Mar 2 at 18:31 | comment | added | Tom Copeland | See eqn. 18 on pg. 4 of “Improved Formula for the Multi-Section of the Linear Three-Term Recurrence Sequence” by Gary Detlefs, Wolfdieter Lang arxiv.org/abs/2304.12937. | |
| Mar 2 at 18:02 | comment | added | Tom Copeland | See also oeis.org/A127672. | |
| Mar 1 at 0:38 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Added tangential connection to generalized Fibonacci polynomials
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| Apr 15, 2023 at 3:59 | comment | added | Tom Copeland | For item F, see also "Rational associahedra and noncrossing partitions" by Armstrong, Rhoades, and Williams and "Rational parking functions and Catalan numbers" by Armstrong, Loehr, and Warrington. | |
| Apr 14, 2023 at 20:35 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Added new refs and interpretations
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| Sep 18, 2021 at 15:07 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Jun 13, 2021 at 15:23 | comment | added | Tom Copeland | See "The Bernoulli numbers and the Riemann zeta function" by Sury for examples for p prime. | |
| Jun 11, 2021 at 5:04 | comment | added | Tom Copeland | For a prime $p$, the sum of the divisors of $p^n$ is $\frac{p^{n+1}-1}{p-1}$. | |
| Aug 5, 2020 at 16:13 | comment | added | Tom Copeland | P. 2252 of "On the zeros of certain polynomials" by Rodriguez-Villegas | |
| Jul 25, 2020 at 19:38 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Added more associations
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jan 5, 2019 at 19:11 | comment | added | Tom Copeland | See also p. 19 of "Iwasawa Theory: A Climb up the Tower" by Sharifi. | |
| Dec 30, 2018 at 22:58 | comment | added | Tom Copeland | The o.g.f. of the multiplicative inverse of each p'th cyclotomic polynomial is a periodic binary sequences of period p. See the OEIS, in particular oeis.org/A010892. | |
| Jul 8, 2018 at 0:06 | comment | added | Tom Copeland | See also "Carries, Combinatorics, and an Amazing Matrix" by John M. Holte (jstor.org/stable/2974981?seq=1#page_scan_tab_contents) for combinatorics associated to powers of the polynomials. | |
| Jan 11, 2017 at 22:44 | comment | added | Tom Copeland | See also the bivariate complete homogeneous symmetric polynomials, the h-polynomials of the (n-1)-simplices, discussed in oeis.org/A135278 and on pg. 43 of "An inversion theorem for labelled trees ..." by Drake (people.brandeis.edu/~gessel/homepage/students/drakethesis.pdf). | |
| Dec 24, 2016 at 8:29 | comment | added | Tom Copeland | See Eqn. 2.1.1 on p. 5 of "The discriminant and the determinant of a hypersurface of even dimension" by Saito (arxiv.org/abs/1110.1717). | |
| Dec 23, 2016 at 21:34 | comment | added | Tom Copeland | See Egn. 5.3 on p. 22 of "Feynman motives and deletion-contraction relations" by Aluffi and Marcolli arxiv.org/abs/0907.3225 | |
| Oct 4, 2016 at 13:31 | comment | added | Tom Copeland | See Eqn. 3 of "Polygons and Chaos" by Kappraff amd Adamson archive.bridgesmathart.org/2001/bridges2001-67.pdf, and Eqn, 2.33 page 14 of "Transfer matrices ... Potts model. VI. ..." by Salas and Sokal arxiv.org/abs/1002.3761. | |
| Oct 18, 2014 at 1:48 | comment | added | Tom Copeland | A059260 (A239473) now has a combinatorial interpretation.--For p prime, these are the h-polynomials for the n-simplexes.--Confer A049019 to see how substituting an e.g.f. for x can be used to generate a partition polynomial for the faces of permutahedra. | |
| Oct 12, 2014 at 6:10 | history | edited | Tom Copeland | CC BY-SA 3.0 |
A relation to Chebyshev polynomials
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| Apr 14, 2014 at 2:42 | history | edited | Tom Copeland | CC BY-SA 3.0 |
More connections
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| Apr 14, 2014 at 2:00 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Expanded relations
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| Apr 9, 2014 at 10:16 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Other connections to combinatorics
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| Mar 26, 2014 at 10:17 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Whitney number connection
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| Mar 26, 2014 at 3:47 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Another example
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| Mar 25, 2014 at 13:22 | history | edited | Tom Copeland | CC BY-SA 3.0 |
added 100 characters in body
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| Mar 22, 2014 at 15:48 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Expanded discussion
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| Mar 22, 2014 at 15:12 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Expanded discussion
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| Mar 22, 2014 at 6:16 | history | answered | Tom Copeland | CC BY-SA 3.0 |