OEIS/Tilings: Difference between revisions
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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 | * 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, ''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 | |||
===New format=== | ===New format=== | ||
This encoding uses uppercase and lowercase letters only. k-uniformity is encoded by chr(ord('A') - 1 + k). | This encoding uses uppercase and lowercase letters only. k-uniformity is encoded by chr(ord('A') - 1 + k). | ||
Revision as of 10:12, 15 May 2020
Generating functions of coordination sequences
- Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers
- Chaim Goodman-Strauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121-134, also on NJAS's home page. Also " arXiv:1803.08530.
- M.[ichael P.] Benson, Growth series of finite extensions of Zn are rational, Invent. Math. 73 (1983), no. 2, 251–269. MR 714092
- Branko Grunbaum and Geoffrey C. Shephard, Tilings by Regular Polygons, Mathematics Magazine, Vol. 50, No. 5 (Nov., 1977), pp. 227-247
- Sean A. Irvine, 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.
- Ralf W. Grosse-Kunstleve, Zeolites, Frameworks, Coordination Sequences & Encyclopedia of Integer Sequences, 1006
New format
This encoding uses uppercase and lowercase letters only. k-uniformity is encoded by chr(ord('A') - 1 + k). 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.