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Trees without twin-leaves with smallest number of maximal independent sets
Discrete Mathematics and Applications. 2020. Vol. 30. No. 1. P. 53–67.
For any n, in the set of n-vertex trees such that any two leaves have no common adjacent vertex, we describe the trees with the smallest number of maximal independent sets.
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Ignatov D. I., , in: 17th International Conference, ICFCA 2023, Kassel, Germany, July 17–21, 2023, Proceedings. Formal Concept Analysis, (LNCS, volume 13934).: Switzerland: Springer, 2023. P. 152–165.
There are well-known problems in extremal set theory that can be formulated as enumeration of the maximal independent sets or counting their total number in certain graphs. Here we provide an FCA-based solution on the number of maximal independent sets of the covering graph of a hypercube. In addition, we consider the related maximal independence ...
Added: November 23, 2023
D. S. Taletskii, Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2023 Vol. 17 No. 1 P. 213–224
The minimum total dominating set (MTDS) of a graph is a vertex subset D of
minimum cardinality such that every vertex of the graph is adjacent to at least one vertex of D.
In this paper we obtain a sharp upper bound for the number of MTDSs in the class
of n-vertex 2-caterpillars. We also show that for ...
Added: April 25, 2023
Taletskii D., Дискретный анализ и исследование операций 2023 Т. 30 № 1 С. 110–129
The minimum total dominating set (MTDS) of a graph is a vertex subset D of minimum cardinality such that every vertex of the graph is adjacent to at least one vertex of D. In this paper we obtain the sharp upper bound for the number of MTDS in the class of n-vertex 2-caterpillars. We also show that ...
Added: November 15, 2022
Taletskii D., Malyshev D., Discrete Applied Mathematics 2022 Vol. 314 P. 321–330
For any n and l, we completely describe trees with the maximum and minimum numbers of maximal independent sets among all n-vertex trees with l leaves. ...
Added: March 30, 2022
Taletskii D., Malyshev D., Discrete Mathematics and Applications 2021 Vol. 31 No. 2 P. 135–144
A complete description of trees with maximal possible number of maximum independent setsamong all 𝑛-vertex trees with exactly 𝑙 leaves is obtained. For all values of the parameters 𝑛 and 𝑙, the extremal tree is unique and is the result of merging the endpoints of 𝑙 simple paths. ...
Added: April 13, 2021
Busjatskaja I., Kochetkov Y., / Series arXiv "math". 2018. No. 1811.10357.
In this paper we at first consider plane trees with the root vertex and a marked directed edge, outgoing from the root vertex. For such trees we introduce a new characteristic-- the parity, using the bracket code. It turns out that the parity depends only on the root vertex (not on the marked edge). And ...
Added: November 27, 2018
Avdoshin S. M., Набебин А. А., М.: ДМК Пресс, 2019.
The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite ...
Added: August 24, 2018
Taletskii D., Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2018 Vol. 12 No. 2 P. 369–381
For each n and d, we describe the structure of trees with the maximal possible number of greatest independent sets in the class of n-vertex trees of vertex degree at most d. We show that for all even n an extremal tree is unique but uniqueness may fail for odd n; moreover, for d = ...
Added: June 22, 2018
Taletskii D., Malyshev D., Discrete Mathematics and Applications 2017 Vol. 27 No. 5 P. 311–318
We investigate the number of maximal independent sets in q-ary trees of height n, when q is fixed and n tends to infinity. ...
Added: October 14, 2017