Distributive numerals (DN) express how a given quantity is distributed within a set of entities. In a sentence like John and Bill carried three suitcases, the number of suitcases (three in total, or three per person, adding up to six) is often ambiguous. Distributive numerals, a specific subtype within numerals, serve to distinguish these two meanings. Although English does not feature this type of numeral, its function can be compared to the use of each in such a sentence. For example, John and Bill each carried three suitcases (implicating six suitcases total) can be contrasted with the sentence John and Bill carried all three suitcases (implicating only three).
Semantically, these structures consist of two parts: a distributive share and a distributive key. The distributive share is the item of potentially ambiguous number[1] (numeral + NP). The distributive key is the element of the sentence that makes the restrictions of the distribution clear: for example, per agent or per action.
Syntactically, a distributive numeral is subordinate to a nominal or verbal head. If the head is nominal, the distributive numeral quantifies the noun numerically; if verbal, it expresses degree. [2]
Types:
NoDN: Distributive numerals do not exist in the language.
DN(N): Distributive numerals can only occur within nominal[3] heads. [4]
DN(V): Distributive numerals can only occur within verbal heads.[5]
Dupl(DN): Reduplication of the stem of a numeral can occur within either nominal or verbal heads.
Dupl(DN)(N): Reduplication of the stem can only occur within nominal heads.
Dupl(DN)(V): Reduplication of the stem can only occur within verbal heads.
Pref(DN): A special prefix, or special prefixes, can attach to the stem within either nominal or verbal heads.
Pref(DN)(N): A special prefix, or special prefixes, can attach to the stem only within nominal heads.
Pref(DN)(V): A special prefix, or special prefixes, can attach to the stem only within verbal heads.
Suf(DN): A special suffix, or special suffixes, can attach to the stem within any phrase.
Suf(DN)(N): A special suffix, or special suffixes, can attach to the stem only within nominal heads.
Suf(DN)(V): A special suffix, or special suffixes, can attach to the stem only within verbal heads.
WN(DN): A special word, including particles and prepositions, can appear before the numeral within either a nominal or verbal head.
WN(DN)(N): A special word, including particles and prepositions, can appear before the numeral only within a nominal head.
WN(DN)(V): A special word, including particles and prepositions, can appear before the numeral only within a verbal head.
NW(DN): A special word, including particles and prepositions, can appear after the numeral within either a nominal or verbal head.
NW(DN)(N): A special word, including particles and prepositions, can appear after the numeral only within a nominal head.
NW(DN)(V): A special word, including particles and prepositions, can appear after the numeral only within a verbal head.
Mix: A combination of strategies is used: such as paradigmatic combinations (distributive numerals that each display multiple strategies, or multiple distributive numerals that are each of a different type), syntactic combinations (simultaneous display of different strategies, such as affixation of the head element or adposition alongside it, reduplication alongside suffixation), and other morphosyntactic strategies not listed above (for example, circumfixation, intercalation, and compounding).[6]
[1] This number may also be ‘one’; consider the Hungarian example Péter és Pál egy-egy bőröndöt hozott be (‘Péter and Pál each brought one suitcase inside.’) The use of reduplication of egy ‘one’ marks the numeral as distributive, making it clear that they carried one suitcase a piece, totaling two.
[2] This distinction can be seen in the following Hungarian examples: Péter és Pál egy-egy bőröndöt hozott be (‘Péter and Pál each brought one suitcase inside’) and Péter egyesével hozta be a bőröndöket (‘Péter brought the suitcases inside one by one’). In both sentences, the distributive share is the suitcases. In the first sentence, the distributive key is Péter and Pál, and the distributive numeral egy-egy, using reduplicating, expresses quantity (specifically, how many suitcases were brought in per person: one). In the second sentence, the distributive key is the verb behoz (‘bring in’), and the distributive numeral egyesével (‘one by one’) expresses degree (specifically, the rate at which the suitcases were brought in: one at a time).
[3] From hereon, nominal refers to nouns and other nominal word classes that function as nouns.
[4] This value may be combined with another value (except NoDN and DN(V)), using the plus (+) sign.
[5] This value may be combined with another value (except NoDN and DN(V)), using the plus (+) sign.
[6] The details should be specified in the commentary. If a language applies different strategies within nominal heads than it does within verbal heads, this alone is not sufficient to classify it as the Mix type. In this case, the types should be combined using an ampersand (&): for example, Dupl(DN)(N)& Suf(DN)(V).