Written: March 2, 2000

Last update: March 7, 2000

This page has links to the seven Maple packages that accompany Doron Zeilberger's paper `Symbol-Crunching with the TRANSFER-MATRIX Method In Order to Count SKINNY Physical Creatures', by Doron Zeilberger .

The available packages are (in order of appearance in the paper):

• MARKOV, a Maple package that finds generating functions that weight-enumerate paths on Combinatorial Markov Chains. To use it, download it as MARKOV, go into Maple, type `read MARKOV:`, and follow the instructions given there.
• ANIMALS, a Maple package that finds generating functions for counting lattice animals (2D site) confined to a strip. To use it, download it as ANIMALS, go into Maple, type `read ANIMALS`, and follow the instructions given there.

• FreeANIMALS, a Maple package that finds generating functions for counting lattice animals (2D site) each of whose vertical cross-sections is of bounded width. To use it, download it as FreeANIMALS, go into Maple, type `read FreeANIMALS`, and follow the instructions given there.

• SAP, a Maple package that finds generating functions for counting self-avoiding polygons in the 2D square-lattice confined to a strip. To use it, download it as SAP, go into Maple, type `read SAP`, and follow the instructions given there.
• FreeSAP, a Maple package that finds generating functions for counting self-avoiding polygons in the 2D square-lattice each of whose vertical cross-sections is of bounded width. To use it, download it as FreeSAP, go into Maple, type `read FreeSAP`, and follow the instructions given there.
• SAW, a Maple package that finds generating functions for counting self-avoiding walks in the 2D square-lattice confined to a strip. To use it, download it as SAW, go into Maple, type `read SAP`, and follow the instructions given there.
• FreeSAW, a Maple package that finds generating functions for counting self-avoiding walks in the 2D square-lattice each of whose vertical cross-sections is of bounded width. To use it, download it as FreeSAW, go into Maple, type `read FreeSAW`, and follow the instructions given there.

## Sample Input and Output Files

### For ANIMALS:

In order to find the generating functions run First Input File for ANIMALS, and you should get First Output File for ANIMALS

In order to find the series expansions for the generating functions, run Second Input File for ANIMALS, and you should get Second Output File for ANIMALS

In order to find the series expansion for the (unrestricted) ANIMAL Series run Third Input File for ANIMALS, and you should get Third Output File for ANIMALS

### Input and Output Files for FreeANIMALS:

In order to find the generating functions run First Input File for FreeANIMALS, and you should get First Output File for FreeANIMALS

In order to find the series expansions for the generating functions, run Second Input File for FreeANIMALS, and you should get Second Output File for FreeANIMALS

In order to find a new rigorous lower bound for Klarner's constant, run Third Input File for FreeANIMALS, and after 27000 secs. of CPU time, you should get Third Output File for FreeANIMALS

### For SAP:

In order to find the generating functions run First Input File for SAP, and you should get First Output File for SAP

In order to find the series expansions for the generating functions, run Second Input File for SAP, and you should get Second Output File for SAP

In order to find the series expansion for the (unrestricted) SAP Series run Third Input File for SAP, and you should get Third Output File for SAP

### For FreeSAP:

In order to find the generating functions run First Input File for FreeSAP, and you should get First Output File for FreeSAP

In order to find the series expansions for the generating functions, run Second Input File for FreeSAP, and you should get Second Output File for FreeSAP

### For SAW:

In order to find the generating functions run First Input File for SAW, and you should get First Output File for SAW

In order to find the series expansions for the generating functions, run Second Input File for SAW, and you should get Second Output File for SAW

In order to find the series expansion for the (unrestricted) SAW Series run Third Input File for SAW, and you should get Third Output File for SAW

### For FreeSAW:

In order to find the generating functions run First Input File for FreeSAW, and you should get First Output File for FreeSAW

In order to find the series expansions for the generating functions, run Second Input File for FreeSAW, and you should get Second Output File for FreeSAW

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