We obtain new results on minimum lengths of words in an unavoidable set of words of cardinality n before introducing the notion of aperiodic unavoidable sets, a natural extension of unavoidable sets.â€¦ (More)

Let a finite semilattice S be a chain under its natural order. We show that if a semigroup T divides a semigroup of full order preserving transformations of a finite chain, then so does anyâ€¦ (More)

The relative rank rank(S : U) of a subsemigroup U of a semigroup S is the minimum size of a set V âŠ† S such that U together with V generates the whole of S. As a consequence of a result by SierpiÅ„skiâ€¦ (More)

In this paper we introduce certain order-preserving partial mappings associated with the letters of a primitive word and examine the semigroup thereby generated. The partial mappings act on anâ€¦ (More)

Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regularâ€¦ (More)

For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappingsOX on X modulo the full transformation semigroup TX . In other words, we ask what is theâ€¦ (More)

For standard terms in semigroup theory see, for example, [5, 8, 12]. Let Xn denote the chain Xn = {1, 2, . . . , n} considered with the standard order. Let Tn denote the full transformation semigroupâ€¦ (More)

This report is based on a study of acute infections of the upper respiratory tract in 1965 and detailed records of such infections in 1963 and 1964. A change from illnesses mainly yielding viruses toâ€¦ (More)

India has been perceived as a development enigma: Recent rates of economic growth have not been matched by similar rates in health and nutritional improvements. To meet the second Sustainableâ€¦ (More)