Direct-sum conjecture for transversal q-matroids

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Let M1M_1 and M2M_2 be transversal qq-matroids with presentations X1\mathcal{X}_1 and X2\mathcal{X}_2. Their direct sum is denoted by M1ameoplusM2M_1 ame{oplus}M_2, and the corresponding combined presentation is denoted by X1ameoplusX2\mathcal{X}_1 ame{oplus}\mathcal{X}_2.

Direct-sum conjecture for transversal q-matroids. The direct sum M1⊕M2M_1\oplus M_2 is a transversal qq-matroid with presentation X1⊕X2\mathcal{X}_1\oplus\mathcal{X}_2.

The conjecture would extend the established coordinate case to arbitrary transversal qq-matroids and provide an analogous construction of presentations under direct sums. Its resolution is not supplied in the source.

References

Primary source

Andrew Fulcher, “A cyclic flat embedding theorem for transversal q-matroids”, arXiv:2603.13550 (2026).

Additional references

3 papers in this index state this conjecture (2003–2026). The statement above is taken from the most recent of them; the others are arXiv:1111.5291, arXiv:math/0305418.

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