Home page of Dr Iwan Jensen ARC Research Fellow Statistical Mechanics and Combinatorics Group Department of Mathematics and Statistics

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 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

• 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

  • Mean-squared radius of gyration:

    Convex

    Directed and Convex

    Staircase

    Stack

    Ferrer's diagrams

    Rectangles

• 2-convex polygons on the square lattice:

  • Enumerations by perimeter:

    The anisotropic GF in Maple friendly format

• 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 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

Created:  24 April, 2000
Last modified: 14 September, 2003