Related papers: Hirotaka's problem 028
The Sudoku puzzle has achieved worldwide popularity recently, and attracted great attention of the computational intelligence community. Sudoku is always considered as Satisfiability Problem or Constraint Satisfaction Problem. In this…
Some problems of testology are discussed.
The generalised Sudoku problem with $N$ symbols is known to be NP-complete, and hence is equivalent to any other NP-complete problem, even for the standard restricted version where $N$ is a perfect square. In particular, generalised Sudoku…
Global solutions to the obstacle problem were first completely classified in two dimensions by Sakai using complex analysis techniques. Although the complex analysis approach produced a very succinct proof in two dimensions, it left the…
We construct a countable inductive limit of weighted Banach spaces of holomorphic functions, which is not a topological subspace of the corresponding weighted inductive limit of spaces of continuous functions. The main step of our…
This collection of problems and conjectures is based on a subset of the open problems from the seminar series and the problem sessions of the Institut Mitag-Leffler programme Graphs, Hypergraphs, and Computing. Each problem contributor has…
We review and investigate some new problems and results in the field of dynamical systems generated by iteration of maps, {\beta}-transformations, partitions, group actions, bundle dynamical systems, Hasse-Kloosterman maps, and some aspects…
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal…
The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of…
We describe a class of combinatorial design problems which typically occur in professional sailing league competitions. We discuss connections to resolvable block designs and equitable coverings and to scheduling problems in operations…
This article is concerned with an example of complex planar geometry arising from flat origami challenges. The complexity of solution algorithms is illustrated, depending on the depth of the initial analysis of the problem, starting from…
This paper presents fifteen problems about mapping class groups. It is an expanded and updated version of the author's preprint "Ten problems on the mapping class groups". The paper will appear in the book "Problems on Mapping Class Groups…
An N=1 supersymmetric system is constructed and its integrability is shown by obtaining three soliton solutions for it using the supersymmetric version of Hirota's direct method.
Hirota's bilinear method ("direct method") has been very effective in constructing soliton solutions to many integrable equations. The construction of one- and two-soliton solutions is possible even for non-integrable bilinear equations,…
We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…
We solve problems 85 a(nd 87 from Birkhoff's book "Lattice Theory" (3rd edition)
We show that single-digit "Nishio" subproblems in nxn Sudoku puzzles may be solved in time o(2^n), faster than previous solutions such as the pattern overlay method. We also show that single-digit deduction in Sudoku is NP-hard.
Inspired by the the Kourovka Notebook of unsolved problems in group theory [KhukhMaz2024], this is a notebook of unsolved problems in the combinatorics of tableaux. Contributions to the notebook are invited.
In this article we study domino snake problems on finitely generated groups. We provide general properties of these problems and introduce new tools for their study. The first is the use of symbolic dynamics to understand the set of all…
The composite plate problem is an eigenvalue optimization problem related to the fourth order operator $(-\Delta)^2$. In this paper we continue the study started in [10], focusing on symmetry and rigidity issues in the case of the hinged…