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===Generating functions of coordination sequences ===
===Generating functions of coordination sequences ===
* Brian Galebach, ''[https://oeis.org/A250120/a250120.html k-uniform tilings (k <= 6) and their A-numbers]''
* Brian Galebach, ''[https://oeis.org/A250120/a250120.html k-uniform tilings (k <= 6) and their A-numbers]''
* Chaim Goodman-Strauss and N. J. A. Sloane, ''[https://doi.org/10.1107/S2053273318014481 A Coloring Book Approach to Finding Coordination Sequences]'', Acta Cryst. A75 (2019), 121-134, also [http://NeilSloane.com/doc/Cairo_final.pdf on NJAS's home page]. Also [http://arxiv.org/abs/1803.08530" arXiv:1803.08530].
* Chaim Goodman-Strauss and N. J. A. Sloane, ''[https://doi.org/10.1107/S2053273318014481 A Coloring Book Approach to Finding Coordination Sequences]'', Acta Cryst. A75 (2019), 121-134, also [http://NeilSloane.com/doc/Cairo_final.pdf on NJAS's home page]. Also [http://arxiv.org/abs/1803.08530 arXiv:1803.08530].
* M.[ichael P.] Benson, ''Growth series of finite extensions of '''Z'''n are rational'', Invent. Math. 73 (1983), no. 2, 251–269. MR 714092
* M.[ichael P.] Benson, ''Growth series of finite extensions of '''Z'''n are rational'', Invent. Math. 73 (1983), no. 2, 251–269. MR 714092
* Branko Grunbaum and Geoffrey C. Shephard, ''[https://www.jstor.org/stable/2689529?seq=4#metadata_info_tab_contents Tilings by Regular Polygons]'', Mathematics Magazine, Vol. 50, No. 5 (Nov., 1977), pp. 227-247
* Branko Grunbaum and Geoffrey C. Shephard, ''[https://www.jstor.org/stable/2689529?seq=4#metadata_info_tab_contents Tilings by Regular Polygons]'', Mathematics Magazine, Vol. 50, No. 5 (Nov., 1977), pp. 227-247
* Sean A. Irvine, ''[https://oeis.org/A008000/a008000_1.pdf Generating Functions for Coordination Sequences of Zeolites after Grosse-Kunstleve, Brunner, and Sloane]'' (with coefficients of many g.f.s)
* Sean A. Irvine, ''[https://oeis.org/A008000/a008000_1.pdf Generating Functions for Coordination Sequences of Zeolites after Grosse-Kunstleve, Brunner, and Sloane]'' (with coefficients of many g.f.s)
* R. W. Grosse-Kunstleve, G. O. Brunner, and N. J. A. Sloane, ''Algebraic description of coordination sequences and exact topological densities for zeolites''. Acta Cryst., A52:879–889, 1996.
* R. W. Grosse-Kunstleve, G. O. Brunner, and N. J. A. Sloane, [https://oeis.org/A005897/a005897.html ''Algebraic description of coordination sequences and exact topological densities for zeolites'']. Acta Cryst., A52:879–889, 1996.
* Ralf W. Grosse-Kunstleve, ''[https://oeis.org/A005897/a005897.html Zeolites, Frameworks, Coordination Sequences & Encyclopedia of Integer Sequences]'', 1006
* Ralf W. Grosse-Kunstleve, ''[https://oeis.org/A005897/a005897.html Zeolites, Frameworks, Coordination Sequences & Encyclopedia of Integer Sequences]'' (a005897.html), 1996
===New format===
* [https://commons.wikimedia.org/wiki/Wallpaper_group_diagrams Wallpaper group diagrams]
This encoding uses uppercase and lowercase letters only. k-uniformity is encoded by chr(ord('A') - 1 + k).
* cf. also '''[[OEIS/coors|coors]]'''
The possible vertex types are encoded as follows:
A: 3.3.3.3.3.3
B: 3.3.3.3.6
C: 3.3.3.4.4
D: 3.3.4.3.4
E: 3.3.4.12
F: 3.3.6.6
G: 3.4.3.12
H: 3.4.4.6
I: 3.4.6.4
J: 3.6.3.6
K: 3.12.12
L: 4.4.4.4
M: 4.6.12
N: 4.8.8
O: 6.6.6
 
Corresponding lowercase letters are used if the orientation of the target vertex is opposite to the orientation of the focus vertex.

Latest revision as of 20:39, 27 May 2020

Generating functions of coordination sequences

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