26 citations · 65 across the 15 of their papers we have counts for
7 papers · 1 filter
Shuffle Squares in Differentiable Words
Michał Zwierzyński
Experiments on binary run-length differentiability lead to sharp computer-assisted criteria for shuffle squares. Every -word of length greater than is a shuffle square ex…
Singularities of the Wigner Caustic and the Centre Symmetry Set of Frontal Curves in the Euclidean Plane
Michał Zwierzyński
Motivated by the role of the Wigner caustic in semiclassical phase-space analysis, we extend it, together with the centre symmetry set, from regular planar curves to cooriented fro…
Invariants of an Affine Reflection Transform
Peter Giblin, Stanisław Janeczko, Michał Zwierzyński
We introduce the affine reflection transform (ART) of an oval relative to an interior point by applying the parallel-tangent involution to chords through and taking the…
A Sharp Surface-Area Extension of Vaaler's Theorem
Michał Zwierzyński
Karasev proved, in dimensions two and three, a sharp surface-area counterpart of a polyhedral extension of Vaaler's theorem [8, Theorem 1.2]. We remove the dimension restriction. M…
Area-Normalized Pentagram Map Dynamics: Spectral Flattening and Elliptic Asymptotics
Michał Zwierzyński
The pentagram map sends a polygon to the intersections of consecutive short diagonals. We study its shape dynamics after translating and positively rescaling each iterate to restor…
Mixed Volumes, the Wigner Caustic, and Isoperimetric Inequalities
Michał Zwierzyński
Let be a convex body and its central symmetral. We study the defects through the even--odd decomp…
Convex Polygons with Parallel Opposite Sides: Convergence, Reconstruction, and Isoperimetric Inequalities
Izabella Konicer, Bartłomiej Murawski, Bruno Rogala +2
In this paper, we study affine -equidistants of convex polygons with parallel opposite sides (CPPOSes), introduced by M. Craizer et al. (Polygons with Parallel Opposite Sides, D…