Literature by the same author
plus at Google Scholar

Bibliografische Daten exportieren
 

Simple games with minimum

Title data

Kurz, Sascha ; Samaniego, Dani:
Simple games with minimum.
Bayreuth , 2025 . - 16 p.
DOI: https://doi.org/10.15495/EPub_UBT_00008169

Official URL: Volltext

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