at Google ScholarTitle data
Kurz, Sascha ; Samaniego, Dani:
Simple games with minimum.
Bayreuth
,
2025
. - 16 p.
DOI: https://doi.org/10.15495/EPub_UBT_00008169
Abstract in another language
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 |
| 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 |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Date Deposited: | 08 Feb 2025 22:00 |
| Last Modified: | 10 Feb 2025 06:46 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/92325 |