Related papers: River Crossing Problems: Algebraic Approach
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Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful…
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must…
A comprehensive review of the literature on crossover design is needed to highlight its evolution, applications, and methodological advancements across various fields. Given its widespread use in clinical trials and other research domains,…
When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to…
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Kin selection theory is a kind of causal analysis. The initial form of kin selection ascribed cause to costs, benefits, and genetic relatedness. The theory then slowly developed a deeper and more sophisticated approach to partitioning the…
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Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In…
We give a solution of the following combinatorial problem: "Let one from $n$ married couples in the m\'enage problem (see Problem 1) be a couple of a known mathematician $M$ and his wife. After the ladies are seated at every other chair,…
Arithmetic differential equations are analogues of algebraic differential equations in which derivative operators acting on functions are replaced by Fermat quotient operators acting on numbers. Now, various remarkable transcendental…
Motivated by the study of word problems of monoids, we explore two ways of viewing binary relations on $A^*$ as languages. We exhibit a hierarchy of classes of binary relations on $A^*$, according to the class of languages the relation…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
Weanalyzethecomputationalcomplexityofanalgorithmtosolve the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most…
The logistics industry is widely regarded as a promising application domain for emerging optimization paradigms, including quantum computing. The Rider-Order Assignment problem is a practically motivated optimization problem arising in…
I discuss the historical roots of the landscape problem and propose criteria for its successful resolution. This provides a perspective to evaluate the possibility to solve it in several of the speculative cosmological scenarios under study…
Applying Baaz's Generalization Method and a new technique to, respectively, proofs and denumerable simple graphs, diverse arithmetical patterns are observed. In particular, sufficient conditions for a number to be a divisor of a Fermat…
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