S. Slobodianiuk

most citedOn the subset Combinatorics of G-spaces

8 citations · 19 across the 4 of their papers we have counts for

collaborators

5 papers

math.GR2014★ 8 cited

On the subset Combinatorics of G-spaces

Igor Protasov, Sergii Slobodianiuk

Let $G$ be a group and let $X$ be a transitive $G$ -space. We classify the subsets of $X$ with respect to a translation invariant ideal $J$ in the Boolean algebra of all s…

math.GR2014

Partitions of groups

Igor Protasov, Sergii Slobodianiuk

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

math.GN2014★ 6 cited

Classifying homogeneous cellular ordinal balleans up to coarse equivalence

Taras Banakh, Igor Protasov, Dusan Repovs +1

For every ballean $X$ we introduce two cardinal characteristics $co v^{♭} (X)$ and $co v^{♯} (X)$ describing the capacity of balls in $X$ . We observe that these cardinal character…

math.GR2014★ 1 cited

A conjecture on partitions of groups

Igor Protasov, Sergii Slobodianiuk

We conjecture that every infinite group $G$ can be partitioned into countably many cells $G = ⋃_{n \in ω} A_{n}$ such that $co v (A_{n} A_{n}^{- 1}) = ∣ G ∣$ for each $n \in ω$ . Here $cov(A)=\min…

math.GR2014★ 4 cited

A note on partitions of groups

Igor Protasov, Sergii Slobodianiuk

Every infinite group $G$ of regular cardinality can be partitioned $G = A_{1} \cup A_{2}$ so that $G \neq = F A_{1}$ , $G \neq = F A_{2}$ for every subset $F \subset G$ of cardinality $∣ F ∣ < ∣ G ∣$ . The fi…