Signed enumeration of partition matrices matches a subclass of inversion sequences; a subset of improper partition matrices is equinumerous with Motzkin paths.
Flajolet, Combinatorial aspects of continued fractions,Discrete Math.32 (1980), no
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Signed counting of partition matrices
Signed enumeration of partition matrices matches a subclass of inversion sequences; a subset of improper partition matrices is equinumerous with Motzkin paths.