Series Expansions for Self-Avoiding Polygons
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Self-Avoiding Polygons on the square lattice:
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Enumerations by perimeter:
Number of SAP A002931 Radius of gyration A056621 First area weighted moment A056625 Second area weighted moment A056631 1-10th area weighted moments (uuencoded)
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Enumerations by area:
Number of SAP A006724 First perimeter weighted moment A056632 Second perimeter weighted moment A056633 -
Enumerations by perimeter and area:
Number of SAP of given perimeter and any area Data is organised as follows: Column 1 is the perimeter, column 2 is the area and column 3 is the number of SAP of the given perimeter and area. Number of SAP of given area and any perimeter Data is organised as follows: Column 1 is the area, column 2 is the perimeter and column 3 is the number of SAP of the given area and perimeter.
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Self-Avoiding Polygons on the triangular lattice:
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Enumerations by perimeter:
Number of SAP Radius of gyration 1-10th area weighted moments (uuencoded) -
Enumerations by perimeter and area:
Number of SAP of given perimeter and any area Data is organised as follows: Column 1 is the perimeter, column 2 is the area and column 3 is the number of SAP of the given perimeter and area. Number of SAP of given area and any perimeter Data is organised as follows: Column 1 is the area, column 2 is the perimeter and column 3 is the number of SAP of the given area and perimeter.
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Self-Avoiding Polygons on the honeycomb lattice:
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Enumerations by perimeter:
Number of SAP Radius of gyration 1-10th area weighted moments (uuencoded) -
Enumerations by area:
Number of SAP -
Enumerations by perimeter and area:
Number of SAP of given perimeter and any area Data is organised as follows: Column 1 is the perimeter, column 2 is the area and column 3 is the number of SAP of the given perimeter and area. Number of SAP of given area and any perimeter Data is organised as follows: Column 1 is the area, column 2 is the perimeter and column 3 is the number of SAP of the given area and perimeter.
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Osculating Polygons on the square lattice:
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Enumerations by perimeter:
Number of Osculating Polygons Radius of gyration First area weighted moment Second area weighted moment
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Neighbour-Avoiding Polygons on the square lattice:
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Enumerations by perimeter:
Number of NAP Radius of gyration First area weighted moment Second area weighted moment
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Classes of convex polygons on the square lattice:
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Enumerations by perimeter:
Convex Directed and Convex Staircase Stack Ferrer's diagrams Rectangles -
Mean-squared radius of gyration:
Convex Directed and Convex Staircase Stack Ferrer's diagrams Rectangles
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2-convex polygons on the square lattice:
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Enumerations by perimeter:
The anisotropic GF in Maple friendly format
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Punctured Polygons on the square lattice.
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Self-Avoiding Polygons (with SAP holes) by perimeter:
1 hole A056634 2 holes A056638 3 holes A056639 All holes A002931
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Self-Avoiding Polygons (with SAP holes) by area:
1 hole A057406 2 holes A057407 3 holes A057408 All holes A057409
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Staircase Polygons (with Staircase holes) by perimeter:
1 hole A057410 2 holes A057411 3 holes A057412 All holes A057413
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Staircase Polygons (with a Rotated Staircase hole) by perimeter:
1 hole
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Staircase Polygons (with Staircase holes) by area:
1 hole A057414 2 holes A057415 3 holes A057416 All holes A057417
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