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Revision History for A114289

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A114289

Number of combinatorial types of n-dimensional polytopes with n+3 vertices.
(history; published version)

#21 by Bruno Berselli at Wed Sep 16 05:02:00 EDT 2020

STATUS

proposed

approved

#20 by Michel Marcus at Wed Sep 16 03:29:04 EDT 2020

STATUS

editing

proposed

#19 by Michel Marcus at Wed Sep 16 03:29:00 EDT 2020

LINKS

É. Éric Fusy, <a href="httphttps://arxiv.org/abs/math.CO/0511466">Counting d-polytopes with d+3 vertices</a>, arXiv:math/0511466 [math.CO], 2005.

Éric Fusy, <a href="https://doi.org/10.37236/1049">Counting d-polytopes with d+3 vertices</a>, Electron. J. Comb. 13 (2006), no. 1, research paper R23, 25 pp.

Aleksandr Maksimenko, <a href="https://arxiv.org/abs/1904.03638">2-neighborly 0/1-polytopes of dimension 7</a>, arXiv:1904.03638 [math.CO], 2019.

STATUS

approved

editing

#18 by Sean A. Irvine at Tue May 21 18:53:27 EDT 2019

STATUS

proposed

approved

#17 by Michael De Vlieger at Tue May 21 18:40:26 EDT 2019

STATUS

editing

proposed

#16 by Michael De Vlieger at Tue May 21 18:40:25 EDT 2019

LINKS

Aleksandr Maksimenko, <a href="https://arxiv.org/abs/1904.03638">2-neighborly 0/1-polytopes of dimension 7</a>, arXiv:1904.03638 [math.CO], 2019.

STATUS

approved

editing

#15 by Bruno Berselli at Fri Dec 14 04:33:22 EST 2018

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proposed

approved

#14 by Jean-François Alcover at Fri Dec 14 03:48:48 EST 2018

STATUS

editing

proposed

#13 by Jean-François Alcover at Fri Dec 14 03:48:40 EST 2018

MATHEMATICA

terms = 26;

G[x_] = -Log[1 - 2(x^3/(1 - 2x)^2)];

H[x_] = -Log[1 - 2x] + Log[1 - x];

K[x_] = -1/2 x (x - 8x^3 - 1 + 5x^2 - 7x^4 + 2x^6 + 5x^8 - 9x^7 + 19x^5 - 14x^9 + x^10 + 19x^11 - 5x^12 + 4x^14 - 8x^13)/(1-x)^5/(2x^6 - 4x^4 + 4x^2 - 1)/(x+1)^2;

1/(x^3 - x^4) (1/4 Sum[EulerPhi[2r + 1]/(2r + 1) G[x^(2r + 1)], {r, 0, terms+2}] + 1/2 Sum[EulerPhi[r]/r H[x^r], {r, 1, terms+2}] + K[x]) + O[x]^(terms+2) // CoefficientList[#, x]& // Rest // Most // Round (* Jean-François Alcover, Dec 14 2018 *)

STATUS

approved

editing

#12 by Joerg Arndt at Sat Aug 15 07:57:43 EDT 2015

STATUS

proposed

approved