* ''P'' isIn [[graded poset|graded]] and [[locally finite posetmathebjkchvxzbcvxdxzvsxvbxvxb|locally finite]] with a unique minimal element;▼
In [[mathematics]], a '''differential poset''' is a [[partially ordered set]] (or ''poset'' for short) satisfying certain local properties. (The formal definition is given below.) This family of posets was introduced by {{harvtxt|Stanley|1988}} as a generalization of [[Young's lattice]] (the poset of [[integer partition]]s ordered by inclusion), many of whose [[combinatorics|combinatorial]] properties are shared by all differential posets. In addition to Young's lattice, the other most significant example of a differential poset is the [[Young–Fibonacci lattice]].
==Definitions==
A poset ''P'' is said to be a differential poset, and in particular to be ''r''-differential (where ''r'' is a positive integer), if it satisfies the following conditions:
▲* ''P'' is [[graded poset|graded]] and [[locally finite poset|locally finite]] with a unique minimal element;
* for every two distinct elements ''x'', ''y'' of ''P'', the number of elements [[covering relation|covering]] both ''x'' and ''y'' is the same as the number of elements covered by both ''x'' and ''y''; and
* for every element ''x'' of ''P'', the number of elements covering ''x'' is exactly ''r'' more than the number of elements covered by ''x''.
