26 citations · 65 across the 15 of their papers we have counts for
18 papers
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…
The th Order Preserving Sets and Isoperimetric Type Inequalities for Planar Ovals
Maksymilian Filip Safarewicz, Michał Zwierzyński
In this work, we introduce and investigate a new class of sets, the \textit{th Order Preserving Sets}, arising naturally from the Fourier analysis of support functions associate…
Artistic Aspects of the Wigner Caustic and the Centre Symmetry Set
Iza Danielewska, Dawid Poławski, Dominika Sterczewska +1
The Wigner caustic and the Centre Symmetry Set of a closed smooth planar curve are known singular sets which generically admit only cusp singularities. Applications of these object…
The Geometry of the Centre Symmetry Set of a Planar Curve
Dominika Miller, Michał Zwierzyński
The Centre Symmetry Set of a planar curve is the envelope of affine chords of , i.e. the lines joining points on with parallel tangent lines. In this paper we study glob…
The Singular Evolutoids Set and the Extended Evolutoids Front
M. Zwierzyński
In this paper we introduce the notion of the singular evolutoid set which is the set of all singular points of all evolutoids of a fixed smooth planar curve with at most cusp singu…
Singular points of the Wigner caustic and affine equidistants of planar curves
W. Domitrz, M. Zwierzyński
In this paper we study singular points of the Wigner caustic and affine --equidistants of planar curves based on shapes of these curves. We generalize the Blaschke-Süss theorem…
The Geometry of the Secant Caustic of a Planar Curve
W. Domitrz, M. C. Romero Fuster, M. Zwierzyński
The secant caustic of a planar curve is the image of the singular set of the secant map of . We analyse the geometrical properties of the secant caustic of a planar curve, i…
The Gauss-Bonnet Theorem for coherent tangent bundles over surfaces with boundary and its applications
Wojciech Domitrz, Michał Zwierzyński
In [31,32,33] the Gauss-Bonnet formulas for coherent tangent bundles over compact oriented surfaces (without boundary) were proved. We establish the Gauss-Bonnet theorem for cohere…
Isoperimetric equalities for rosettes
M. Zwierzyński
In this paper we study the isoperimetric-type equalities for rosettes, i.e. regular closed planar curves with non-vanishing curvature. We find the exact relations between the lengt…
Cubulating mapping tori of some polynomial growth free group automorphisms
Mark Hagen, Daniel T Wise
Let be a finite-rank free group and let have polynomial growth. Let . We give sufficient conditions on that ensure acts fr…
How can a clairvoyant particle escape the exclusion process?
Rangel Baldasso, Augusto Teixeira
We study a detection problem in the following setting: On the one-dimensional integer lattice, at time zero, place nodes on each site independently with probability an…
The improved isoperimetric inequality and the Wigner caustic of planar ovals
Michał Zwierzyński
The classical isoperimetric inequality in the Euclidean plane states that for a simple closed curve of the length , enclosing a region of the area …