CombTop – Combinatorial Solutions for Topological Problems

This Web page gathers some software, examples, additional information, and data referred to in my publications related to applying combinatorial methods for solving topological problems. Currently, it contains software and data referred to in the paper An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds by Grzegorz Graff and Paweł Pilarczyk, but I plan to put more information here in the future.

MinPer - a Program for Determining the Minimal Number of Periodic Points

The program minper is a command-line driven utility aimed at computing lower and upper bounds on the minimal number of r-periodic points in the smooth homotopy class of a map on a closed smooth connected and simply-connected manifold of dimension m ≥ 4. In order to run the program, one must open a text terminal emulator (a.k.a. command prompt), use the cd command to enter the directory in which the executable file is located (note the bin subdirectory), and then one must type minper (or ./minper) follow by suitable arguments. If the program is be called without any arguments, it shows brief information on available command-line arguments. The running program can be interrupted with Ctrl-C at any time. Here are a few sample computations one may try:

  • minper -m 6 -r 36 -b 1
  • minper -m 6 -r 36 -b 1 --all
  • minper -s 3 -a 2 -a 2
  • minper -s 3 -a 2 -a 2 --random 10 --verbose
  • minper -m 6 -a 1 -a 1 -a 1 -b 1

A series of computations were conducted for the purpose of illustrating some results (Tables 1 and 2 in the paper). Detailed logs from all the computations are available in the Download section below; a brief summary is contained in the text file results.txt.

Files for Download

The source code of the program minper is available below under the terms of the GNU General Publica License. In general, it is recommended that the program is compiled for each specific system by the user. Compilation with the GCC compiler should be a smooth process, a makefile suitable for both MS-Windows and Unix/Linux/MacOS system is provided; it should be enough to run make in the main directory of the program. Precompiled versions for the current 64-bit Debian GNU/Linux system as well as a 32-bit version for Microsoft Windows are also provided.

  • – the source code of the software library and programs (compressed in Linux; note that if using in another system, conversion of the text files may be necessary)
  • – the program precompiled for the 64-bit Debian GNU/Linux platform (using the GNU C++ 4.7.2 compiler)
  • – the program precompiled for the 32-bit Microsoft Windows platform (using the MinGW 4.7 compiler), together with the necessary DLL files
  • – a collection of logs (saved output of the program) from the computations conducted for the paper