Related papers: On some impossible disentanglement puzzles

We prove some constructive results that on first and maybe even on second glance seem impossible.

In this piece, we examine one variant of the infamous 15 Tile Puzzle and develop a mathematical backing behind why it is unsolvable. Using concepts of permutations, bijectivity, and cycle transpositions, we not only prove how to model this…

This is the sequel to our first paper concerning the balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. We prove the uniqueness of such an embedding. The proof relies on fine estimates of the…

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the…

We give different proofs and prove new results on the non complete solvability of some systems of complex first order p.d.e.'s, especially related to the analysis on CR manifolds.

We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…

We prove the computational intractability of rotating and placing $n$ square tiles into a $1 \times n$ array such that adjacent tiles are compatible--either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as…

This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…

In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…

In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.

In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…

In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objects which have been of great interest in mathematics. We then…

We investigate the complexity of a puzzle that turns out to be NL-complete.

In this paper, we prove the finiteness of the number of integer solutions of the decomposable form inequalities. We also study the number of integer solutions of a sequence of decomposable form inequalities.

We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…

Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split…

Does a given a set of polyominoes tile some rectangle? We show that this problem is undecidable. In a different direction, we also consider tiling a cofinite subset of the plane. The tileability is undecidable for many variants of this…

In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…