@article {Cvetko-Vah:2011:0236-5294:1,
	author = "Cvetko-Vah, Karin and Kokol Bukovsek, Damjana and Kosir, Tomaz and Kudryavtseva, Ganna",
	title = "Semitransitive subsemigroups of the singular part of the finite symmetric inverse semigroup",
	journal = "Acta Mathematica Hungarica",
	volume = "131",
	number = "1-2",
	year = "2011",
	abstract = "We prove that the minimal cardinality of a semitransitive subsemigroup in the singular part &#60;EquationSource Format="TEX"&#62; &#36;mathcal{I}_{n}setminus mathcal{S}_{n}&#36; &#60;/EquationSource&#62; of the symmetric inverse semigroup &#60;EquationSource Format="TEX"&#62; &#36;mathcal{I}_{n}&#36; &#60;/EquationSource&#62; is 2<I>n</I>&#8722;<I>p</I>+1, where <I>p</I> is the greatest proper divisor of <I>n</I>, and classify all semitransitive subsemigroups of this minimal cardinality.",
	pages = "1-24",
	url = "http://www.ingentaconnect.com/content/klu/amhu/2011/00000131/F0020001/00000071",
	doi = "doi:10.1007/s10474-011-0071-9",
	keyword = "symmetric inverse semigroup, singular part, semitransitivity, minimal cardinality, 20M18"
}