Series Expansions for SelfAvoiding Polygons

SelfAvoiding 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 110th 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.


SelfAvoiding Polygons on the triangular lattice:

Enumerations by perimeter:
Number of SAP Radius of gyration 110th 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.


SelfAvoiding Polygons on the honeycomb lattice:

Enumerations by perimeter:
Number of SAP Radius of gyration 110th 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.


Osculating Polygons on the square lattice:

Enumerations by perimeter:
Number of Osculating Polygons Radius of gyration First area weighted moment Second area weighted moment


NeighbourAvoiding 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 
Meansquared radius of gyration:
Convex Directed and Convex Staircase Stack Ferrer's diagrams Rectangles


2convex polygons on the square lattice:

Enumerations by perimeter:
The anisotropic GF in Maple friendly format


Punctured Polygons on the square lattice.

SelfAvoiding Polygons (with SAP holes) by perimeter:
1 hole A056634 2 holes A056638 3 holes A056639 All holes A002931

SelfAvoiding 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 a Rotated Staircase hole) by perimeter:
1 hole

Staircase Polygons (with Staircase holes) by area:
1 hole A057414 2 holes A057415 3 holes A057416 All holes A057417


Imperfect Staircase Polygons on the square lattice.