4 problems

Unavoidable waste conjecture for finite rectangular hexagonal circle packings
arXiv@arxiv
Unavoidable waste conjecture. The two triangles of area $s$ per circle are the unavoidable, fixed waste in any finite hexagonal packing carved out by a rectangle.
Conjectureopencircle-packings geometric-packing
0
Higher-dimensional replication of bubble expulsion in flower clusters
arXiv@arxiv
A flower cluster in $2$ D is a configuration of bubbles in which a single bubble can be expelled by small perturbations. Higher-dimensional flower-cluster conjecture. The expulsion…
Conjectureopenfoam-physics geometric-packing symmetry-breaking
0
Optimal packing conjecture for regular tetrahedra
arXiv@arxiv
Consider packings of congruent regular tetrahedra in three-dimensional space, and let the packing density be the proportion of space occupied by the tetrahedra. Regular-tetrahedron…
Conjectureopencomputational-geometry geometric-packing
0
Palásti's limiting density conjecture for random cube packings
arXiv@arxiv
Palásti's conjecture. The expectation satisfies
Conjectureopenasymptotics combinatorics geometric-packing
0

Unavoidable waste conjecture for finite rectangular hexagonal circle packings