Rota's Unimodality Conjecture for Matroid Flats

Is the sequence $W_0, W_1, \dots, W_n$ counting the flats of each rank of a matroid always unimodal? Rota conjectured yes in 1970.

36Significance / 100

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combinatoricsJul 24, 2026Significance 36/100Registry: unreviewed

Prior state unknown→disproved

Is the sequence $W_0, W_1, \dots, W_n$ counting the flats of each rank of a matroid always unimodal? Rota conjectured yes in 1970.

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Is the sequence $W_0, W_1, \dots, W_n$ counting the flats of each rank of a matroid always unimodal? Rota conjectured yes in 1970.

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