Leonardo Martínez-Sandoval

activity

20232026

collaborators

7 papers

math.CO2026

Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats

Kolja Knauer, Leonardo Martínez-Sandoval, Criel Merino

Beke, Csáji, Csikvári, and Pituk showed that the Merino--Welsh quotient $Φ (M) = T_{M} (1, 1)^{2} / (T_{M} (2, 0) T_{M} (0, 2))$ can be arbitrarily large, so the multiplicative Merino-Welsh inequality…

math.CO2026

Counterexamples and symmetry for uneven orthogonal mass partitions in the plane

Leonardo Martínez-Sandoval

Grünbaum asked whether every planar convex body admits, for every $0 \leq t \leq 1/4$ , two orthogonal lines cutting it into pieces with cyclically ordered areas $t, t, 1/2 - t, 1/2 - t$ . Bá…

math.AT2026

Adjoint reductions of tangent bundles of spheres

Leonardo Martínez-Sandoval

We study reductions of the tangent bundle of $S^{d i m G}$ through the adjoint representation of a compact connected Lie group $G$ . If $d = dim G$ and $r = rank G$ , we s…

math.CO2026

The arc chromatic number for Galois projective planes, affine planes and Euclidean grids

Gabriela Araujo-Pardo, Leonardo Martínez-Sandoval

In 1986, Csima and Füredi determined the minimum number of arcs required to partition the points of Galois projective planes $P G (2, q)$ and affine planes $A G (2, q)$ . We revisit these…

math.CO2025

Hamiltonian connectivity of some base-cobase graphs

Leonardo Martínez-Sandoval, Kolja Knauer

There has been wide interest in understanding which properties of base graphs of matroids extend to base-cobase graphs of matroids. A significant result of Naddef and Pulleyblank (…

math.CO2025

Equicovering masses in the Euclidean plane

Manuel A. Espinosa-García, Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado

Classic mass partition results are about dividing the plane into regions that are equal with respect to one or more measures (masses). We introduce a new concept in which the notio…

math.CO2023

On a colorful problem by Dol'nikov concerning translates of convex bodies

Leonardo Martínez-Sandoval, Edgardo Roldán-Pensado

In this note we study a conjecture by Jerónimo-Castro, Magazinov and Soberón which generalized a question posed by Dol'nikov. Let $F_{1}, F_{2}, \dots, F_{n}$ be families of translates of a…