See @feigin1975characteristic.
Definition
Given a manifold $M$, a flag of foliations of codimensions $q_k\leq q_{k-1}\leq \cdots \leq q_1$ is a sequence of foliations $\mathcal F_1,\ldots,\mathcal F_k$ such that for $i=1,\ldots,k$ the codimension of $\mathcal F_i$ is $q_i$ and for $i\leq j$ the leaves of $\mathcal F_i$ are contained in those of $\mathcal F_j$.
$\blacksquare$
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Author of the notes: Antonio J. Pan-Collantes
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