Replacing the falling factorial with a rising factorial in the expression for bino-
According to Donald Knuth, the  rst study of these objects was performed by Bha skara cha rya, and alternate names for them included  bunch  and  suite . Replacing the falling factorial with a rising factorial in the expression for bino- mial coe cients gives the number of these of a given size with a certain number of elements. The free commutative monoid on a set can be interpreted as the monoid of these things with elements drawn from that set. These things are formally de ned using a set and a function from that set to the   positive integers. For ten points, identify these objects which generalize sets to allow repeated instances of elements.
According to Donald Knuth, the  rst study of these objects was performed by Bha skara cha rya, and alternate names for them included  bunch  and  suite .
multisets [be generous and prompt on sets, also prompt on bags, lists, heaps, samples, weighted sets, and collections, prompt on bunches and suites until they are respectively read]