mathlib3 documentation


Antidiagonals in ℕ × ℕ as multisets #

THIS FILE IS SYNCHRONIZED WITH MATHLIB4. Any changes to this file require a corresponding PR to mathlib4.

This file defines the antidiagonals of ℕ × ℕ as multisets: the n-th antidiagonal is the multiset of pairs (i, j) such that i + j = n. This is useful for polynomial multiplication and more generally for sums going from 0 to n.

Notes #

This refines file data.list.nat_antidiagonal and is further refined by file data.finset.nat_antidiagonal.

The antidiagonal of a natural number n is the multiset of pairs (i, j) such that i + j = n.


A pair (i, j) is contained in the antidiagonal of n if and only if i + j = n.


The cardinality of the antidiagonal of n is n+1.


The antidiagonal of 0 is the list [(0, 0)]


The antidiagonal of n does not contain duplicate entries.