Series Expansions for Self-Avoiding Polygons

• Self-Avoiding Polygons on the square lattice:

• 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)

• 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.

• Self-Avoiding Polygons on the triangular lattice:

• 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.

• Self-Avoiding Polygons on the honeycomb lattice:

• 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.

• Osculating Polygons on the square lattice:

• Enumerations by perimeter:

 Number of Osculating Polygons Radius of gyration First area weighted moment Second area weighted moment
• Neighbour-Avoiding Polygons on the square lattice:

• Enumerations by perimeter:

 Number of NAP Radius of gyration First area weighted moment Second area weighted moment

• Classes of convex polygons on the square lattice:

• Enumerations by perimeter:

 Convex Directed and Convex Staircase Stack Ferrer's diagrams Rectangles

 Convex Directed and Convex Staircase Stack Ferrer's diagrams Rectangles

• Punctured Polygons on the square lattice.

• Self-Avoiding Polygons (with SAP holes) by perimeter:

 1 hole A056634 2 holes A056638 3 holes A056639 All holes A002931

• Self-Avoiding Polygons (with SAP holes) by area:

 1 hole A057406 2 holes A057407 3 holes A057408 All holes A057409

• Staircase Polygons (with Staircase holes) by perimeter:

 1 hole A057410 2 holes A057411 3 holes A057412 All holes A057413

• Staircase Polygons (with Staircase hole) by OUTER perimeter:

 1 hole A173408

• Staircase Polygons (with Staircase holes) by area:

 1 hole A057414 2 holes A057415 3 holes A057416 All holes A057417