All Outputs (2)

The rank of the semigroup of transformations stabilising a partition of a finite set (2015)
Journal Article
Araújo, J., Bentz, W., Mitchell, J., & Schneider, C. (2015). The rank of the semigroup of transformations stabilising a partition of a finite set. Mathematical proceedings of the Cambridge Philosophical Society, 159(02), 339-353. https://doi.org/10.1017/S0305004115000389

Let P be a partition of a finite set X. We say that a full transformation f:X→X preserves (or stabilizes) the partition P if for all P∈P there exists Q∈P such that Pf⊆Q. Let T(X,P) denote the semigroup of all full transformations of X that preserve t... Read More about The rank of the semigroup of transformations stabilising a partition of a finite set.

The commuting graph of the symmetric inverse semigroup (2015)
Journal Article
Araújo, J., Bentz, W., & Janusz, K. (2015). The commuting graph of the symmetric inverse semigroup. Israel journal of mathematics, 207(1), 103-149. https://doi.org/10.1007/s11856-015-1173-9

The commuting graph of a finite non-commutative semigroup S, denoted G(S), is a simple graph whose vertices are the non-central elements of S and two distinct vertices x, y are adjacent if xy = yx. Let I(X) be the symmetric inverse semigroup of parti... Read More about The commuting graph of the symmetric inverse semigroup.