arXiv subjects

Margo Kondratieva

Publications and source records attributed to Margo Kondratieva.

4 recordsLinked to original sources

arXiv2026

The triplication method for constructing strong starters

The triplication method for constructing strong starters in $Z_{3m}$ from starters in $Z_{m}$ (say, a starter of order 21 from a starter of order 7) was proposed by the authors in 2025. The method reduced construction of the particular combinatorial design (a strong starter in a cyclic group) to solving a Sudoku-type problem -- an independent task with its own tools and techniques available. The Sudoku-type problem was formulated in terms of the so-called triplication table constructed from a starter of order $m$. The method was applicable for odd orders $m\ge 7$ not divisible by 3. In the present paper, our previous approach is developed in two directions: (1) the definition of the triplication table is generalized, which expands possibilities for its construction to include three base starters or even ``pseudostarters''; (2) the formulation of the Sudoku-type problem is broadened to embrace various scenarios of ``modular encoding'' and reconstruction of strong starters from its solution. A theoretical gain of these developments consists in the improved understanding of the general structure of the triplication approach. A practical outcome is elimination of the requirement that $m$ be not divisible by 3. This leads to a broader scope of strong starters obtainable by triplication: any latent strong starter of odd order $3m$ can emerge this way.

math.CO↗

arXiv2025

Constructing strong starters of orders $3p$: triplication with SAT solver

A novel approach to building strong starters in cyclic groups of orders $n$ divisible by 3 from starters of smaller orders is presented. A strong starter in $Z_n$ ($n$ odd) is a partition of the set $\{1,2,\dots,n-1\}$ into pairs $\{a_i,b_i\}$ such that all pair sums $a_i+b_i$ are distinct and nonzero modulo $n$ and all differences $\pm(a_i-b_i)$ are distinct and nonzero modulo $n$. A special interest to strong starters of odd orders divisible by 3 is motivated by Horton's conjecture which claims that such starters exist (except when $n=3$ or $9$) but remains unproven since 1989. We begin with a strong starter of order $p$ coprime with 3 and describe an algorithm to obtain a Sudoku-type problem modulo 3 whose solution, if exists, yields a strong starter of order $3p$. The process leading from the original to the final starter is called {\em triplication}. Besides theoretical aspects of the construction, practicality of this approach is demonstrated. A general-purpose constraint-satisfaction (SAT) solver z3 is used to solve the Sudoku-type problem; various performance statistics are presented.

math.CO↗

arXiv2005

Numerical study of high frequency asymptotics of the symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems

A high-frequency asymptotics of the symbol of the Dirichlet-to-Neumann map, treated as a periodic pseudodifferential operator, in 2D diffraction problems is discussed. Numerical results support a conjecture on a universal limit shape of the symbol.

physics.comp-ph↗

arXiv2004

Markov's Transformation of Series and the WZ Method

In a well forgotten memoir of 1890, Andrei Markov devised a convergence acceleration technique based on a series transformation which is very similar to what is now known as the Wilf-Zeilberger (WZ) method. We review Markov's work, put it in the context of modern computer-aided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.

math.CA↗