in the repository
URN to cite this document: urn:nbn:de:bvb:703-epub-8169-4
Title data
Kurz, Sascha ; Samaniego, Dani:
Simple games with minimum.
Bayreuth
,
2025
. - 16 S.
![[thumbnail of minimum_enumeration.pdf]](https://epub.uni-bayreuth.de/style/images/fileicons/application_pdf.png) |
|
||||||||
|
Download (280kB)
|
Abstract
Every simple game is a monotone Boolean function. For the other direction we just have to exclude the two constant functions. The enumeration of monotone Boolean functions with distinguishable variables is also known as the Dedekind's problem. The corresponding number for nine variables was determined just recently by two disjoint research groups. Considering permutations of the variables as symmetries we can also speak about non-equivalent monotone Boolean functions (or simple games). Here we consider simple games with minimum, i.e., simple games with a unique minimal winning vector. A closed formula for the number of such games is found as well as its dimension in terms of the number of players and equivalence classes of players.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Keywords: | simple games; enumeration |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-8169-4 |
| Date Deposited: | 05 Feb 2025 11:03 |
| Last Modified: | 05 Feb 2025 11:03 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/8169 |
Download Statistics