arXiv subjects

Dani Samaniego

Publications and source records attributed to Dani Samaniego.

3 recordsLinked to original sources

arXiv2025

Simple games with minimum

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.

math.CO↗

arXiv2021

A note on simple games with two equivalence classes of players

Many real-world voting systems consist of voters that occur in just two different types. Indeed, each voting system with a {\lq\lq}House{\rq\rq} and a {\lq\lq}Senat{\rq\rq} is of that type. Here we present structural characterizations and explicit enumeration formulas for these so-called bipartite simple games.

math.CO↗

arXiv2017

Schottky Groups over Valuation Rings

Given a non-trivial complete valued field $K$ with value group $Λ$, we construct a $Λ$-tree space associated to $K$ analog of the Bruhat-Tits tree, and locally finite trees associated to compact subsets of the projective line. We propose a definition of hyperbolic matrix and Schottky group over such field $K$. To any such Schottky group $Γ$, we associate a compact set with an action of $Γ$, such that the quotient graph of the associated tree is a finite graph, and $Γ$ is identified with its fundamental group. Finally explain a method to construct such groups. This results extend the classical ones for discrete valuations of Mumford and non-archimedean rank 1 valuations of Gerritzen and Van der Put.

math.AG↗