Results 71 to 80 of about 887,803 (201)
On Constrained Matchings, Stable Under Random Preferences
Random Structures &Algorithms, Volume 67, Issue 4, December 2025.ABSTRACT Colloquially, there are two groups, n$$ n $$ men and n$$ n $$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.
Boris Pittel
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Undecidability of polynomial inequalities in weighted graph homomorphism densities
Forum of Mathematics, SigmaMany problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights.
Grigoriy Blekherman +2 more
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Fast and Slow Mixing of the Kawasaki Dynamics on Bounded‐Degree Graphs
Random Structures &Algorithms, Volume 67, Issue 4, December 2025.ABSTRACT We study the worst‐case mixing time of the global Kawasaki dynamics for the fixed‐magnetization Ising model on the class of graphs of maximum degree Δ$$ \Delta $$. Proving a conjecture of Carlson, Davies, Kolla, and Perkins, we show that below the tree‐uniqueness threshold, the Kawasaki dynamics mix rapidly for all magnetizations. Disproving a
Aiya Kuchukova +3 more
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Internal Phase Separation in Synthetic DNA Condensates
Advanced Science, Volume 12, Issue 41, November 6, 2025.The modular, programmable system of DNA nanostructures developed provides programmatic control over multiphase condensate behavior, enabling mapping onto a predictive Flory‐Huggins model. This combined experimental and theoretical framework will help address open questions in condensate biophysics and facilitate the rational design of functional ...
Diana A. Tanase +5 more
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SPERNER THEOREMS FOR UNRELATED COPIES OF POSETS AND GENERATING DISTRIBUTIVE LATTICES
Ural Mathematical JournalFor a finite poset (partially ordered set) \(U\) and a natural number \(n\), let \(S(U,n)\) denote the largest number of pairwise unrelated copies of \(U\) in the powerset lattice (AKA subset lattice) of an \(n\)-element set.
Gábor Czédli
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Estimates on the decay of the Laplace–Pólya integral
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3360-3379, November 2025.Abstract The Laplace–Pólya integral, defined by Jn(r)=1π∫−∞∞sincntcos(rt)dt$J_n(r) = \frac{1}{\pi }\int _{-\infty }^\infty \operatorname{sinc}^n t \cos (rt) \,\mathrm{d}t$, appears in several areas of mathematics. We study this quantity by combinatorial methods; accordingly, our investigation focuses on the values at integer rs$r{\rm s}$.
Gergely Ambrus, Barnabás Gárgyán
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Degrees and prime power order zeros of characters of symmetric and alternating groups
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3408-3428, November 2025.Abstract We show that the p$p$‐part of the degree of an irreducible character of a symmetric group is completely determined by the set of vanishing elements of p$p$‐power order. As a corollary, we deduce that the set of zeros of prime power order controls the degree of such a character. The same problem is analysed for alternating groups, where we show
Eugenio Giannelli +2 more
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Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case
Discrete Analysis, 2017 Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case, Discrete Analysis 2017:5, 34 pp. Szemerédi's theorem, proved in 1975, asserts that for every positive integer $k$ and every $\delta>0$ there exists $n$ such that every subset
Sean Prendiville
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Symmetric 2‐ ( 35 , 17 , 8 ) Designs With an Automorphism of Order 2
Journal of Combinatorial Designs, Volume 33, Issue 10, Page 399-403, October 2025.ABSTRACT The largest prime p that can be the order of an automorphism of a 2‐ ( 35 , 17 , 8 ) design is p = 17, and all 2‐ ( 35 , 17 , 8 ) designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2‐ ( 35 , 17 , 8 ) designs with automorphisms of an odd prime order p < 17 were classified in Bouyukliev, Fack and Winne and ...
Sanja Rukavina, Vladimir D. Tonchev
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Discrete Analysis, 2017 Quasirandom Cayley graphs, Discrete Analysis 2017:6, 14 pp. An extremely important phenomenon in extremal combinatorics is that of _quasirandomness_: for many combinatorial structures, it is possible to identify a list of deterministic properties, each ...
David Conlon, Yufei Zhao
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