e/Alternating permutation

Information
has gloss	eng: In combinatorial mathematics, an alternating permutation of the set 1, 2, 3, ..., n} is an arrangement of those numbers into an order c1, ..., cn such that no element ci is between ci − 1 and ci + 1 for any value of i and c1< c2. In other words, ci < ci+ 1 if i is odd and ci > ci+ 1 if i is even. For example, the five alternating permutations of 1, 2, 3, 4} are: * 1, 3, 2, 4 * 1, 4, 2, 3 * 2, 3, 1, 4 * 2, 4, 1, 3 * 3, 4, 1, 2 This type of permutation was first studied by Désiré André in the 19th century.
lexicalization	eng: Alternating Permutation
instance of	(noun) act of changing the lineal order of objects in a group permutation

Meaning
Italian
has gloss	ita: In combinatoria, una permutazione alternante o permutazione alternata o permutazione a zig-zag di lunghezza n è una permutazione \langle c_1,c_2,...,c_n\rangle dell'insieme 1, 2, 3, ..., n} tale che nessun componente ci con 1<i<n ha valore compreso fra ci − 1 e ci + 1 .
lexicalization	ita: Permutazione alternata