OEIS/Tilings - Revision history

imported>Gfis at 20:39, 27 May 2020

2020-05-27T20:39:54Z

← Older revision		Revision as of 20:39, 27 May 2020
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	* 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.		* 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]'' (a005897.html), 1996		* Ralf W. Grosse-Kunstleve, ''[https://oeis.org/A005897/a005897.html Zeolites, Frameworks, Coordination Sequences & Encyclopedia of Integer Sequences]'' (a005897.html), 1996
			* [https://commons.wikimedia.org/wiki/Wallpaper_group_diagrams Wallpaper group diagrams]
	* cf. also '''[[OEIS/coors\|coors]]'''		* cf. also '''[[OEIS/coors\|coors]]'''

imported>Gfis: a005897.html

2020-05-21T17:34:10Z

a005897.html

← Older revision		Revision as of 17:34, 21 May 2020
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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===~~		* cf. also '''[[OEIS/coors\|coors]]'''
	~~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.~~

imported>Gfis at 10:12, 15 May 2020

2020-05-15T10:12:02Z

← Older revision		Revision as of 10:12, 15 May 2020
Line 1:		Line 1:
	===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, ''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).

imported>Gfis: email removed

2020-05-14T17:11:24Z

email removed

@@ Line 7: / Line 7: @@
 * 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.
 ===New format===
-On May 02 2020 Brian Galbach wrote:
+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
@@ Line 30: / Line 25: @@
   O: 6.6.6
-Following the vertex type designations, we have alternating sections:
+Corresponding lowercase letters are used if the orientation of the target vertex is opposite to the orientation of the focus vertex.

imported>Gfis: Example

2020-05-11T21:20:16Z

Example

← Older revision		Revision as of 21:20, 11 May 2020
Line 1:		Line 1:
	===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

imported>Gfis at 15:42, 11 May 2020

2020-05-11T15:42:04Z

@@ Line 1: / Line 1: @@
 ===New format===
 On May 02 2020 Brian Galbach wrote:
@@ Line 41: / Line 48: @@
 Finally, class C has connected to it vertex classes A, C, and C.  And the connected edges from each of those vertices are edge 4, edge 3, and edge 2.

imported>Gfis: Created page with "===New format=== On May 02 2020 Brian Galbach wrote: Here's a new file with a very compact and simple code for each tiling. It has several sections separated by semicolons,..."

2020-05-11T10:03:23Z

Created page with "===New format=== On May 02 2020 Brian Galbach wrote: Here's a new file with a very compact and simple code for each tiling. It has several sections separated by semicolons,..."

New page

===New format===
On May 02 2020 Brian Galbach wrote:

Here's a new file with a very compact and simple code for each tiling. It has several sections separated by semicolons, which I will explain below.

Each code starts with a single capital letter representing the uniformity of the tiling. A is 1-uniform, B is 2-uniform, etc.

Next, we have a letter representing the vertex type for each vertex class in the tiling. These are 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

Following the vertex type designations, we have alternating sections:

The first section describes the classes connected to class A. The number of connections must of course be the same as the number of polygons in class A. And each connected class must be from A to the nth letter of the alphabet, where our tiling is n-uniform. (Important: Do not confuse the vertex type, which is A to O, with the vertex class, which is A, B, or C in a 3-uniform tiling, for example.)

The second section describes the orientation of each of those vertices connected to class A. The letter, whether it is uppercase or lowercase, gives us the edge of the connected vertex that is connected to the current edge. A or a is the first edge, B or b is the second edge, etc. And uppercase means that the direction of rotation of the connected vertex is the same as the current vertex, while lowercase means that the direction of rotation is reversed.

Then we repeat the above two sections for class B, class C, etc.

That's it. Let's do an example just so this is clear. I'll pick a line pretty much at random. Okay, this one:
C;FJO;BABC;BBAA;AABB;CADC;ACC;DCB

So we have a 3-uniform tiling (C). The three vertex classes have the vertex types 3.3.6.6, 3.6.3.6, and 6.6.6 (FJO).

Now let's look at vertex class A. It has connected to it vertex classes B, A, B, and C. And the edges connected from each of those vertices are edge 2, edge 2, edge 1, and edge 1. And since these are all uppercase letters, there is no reversing of the direction of rotation relative to the direction of our central vertex.

Class B has connected to it vertex classes A, A, B, and B. And the connected edges are edge 3, edge 1, edge 4, and edge 3, and no direction reversal.

Finally, class C has connected to it vertex classes A, C, and C. And the connected edges from each of those vertices are edge 4, edge 3, and edge 2.