Results 121 to 130 of about 37,501 (244)
Determinants, choices and combinatorics [PDF]
Discrete Mathematics, 2019 We prove a formula which generalizes both Onn's colorful determinantal formula, related to Rota's basis conjecture, and Svrtan's $n!$ formula, related to the Atiyah-Sutcliffe problem. In some cases, our formula allows us to prove some results similar in spirit to the statement of Rota's basis conjecture.
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Universal properties of Delannoy categories
Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.Abstract Recently, Harman and Snowden introduced a new symmetric tensor category Perm̲(G,μ)$\operatorname{\underline{Perm}}(G, \mu)$ associated with an oligomorphic group G$G$ with a measure μ$\mu$. When G$G$ is the group of order‐preserving self‐bijections of the real line there are four such measures, and the resulting tensor categories are called ...
Kevin Coulembier +2 more
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Sharp restriction estimates for some degenerate higher codimensional quadratic surfaces
Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.Abstract The Fourier restriction conjecture is a fundamental problem in harmonic analysis. In this paper, we investigate restriction estimates for degenerate higher codimensional quadratic surfaces and obtain sharp results for some types of degenerate cases.
Zhenbin Cao, Changxing Miao, Yixuan Pang
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Combinatorics, Words and Symbolic Dynamics
, 2016 Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise ...
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Bounded exponential sums with multiplicative coefficients
Mathematika, Volume 72, Issue 4, October 2026.Abstract We investigate when the exponential sum Sf(x,α):=∑n⩽xf(n)e(nα)$S_f(x,\alpha) := \sum _{n\leqslant x}f(n)\mathrm{e}(n\alpha)$ is bounded, for a multiplicative function f$f$ and α∈R$\alpha \in \mathbb {R}$. We show that under natural assumptions, Sf(x,α)$S_f(x,\alpha)$ is bounded only when f$f$ is very close to a twisted Dirichlet character χ(n ...
Péa Bazin, Ihor Pylaiev, Fred Tyrrell
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Abelian number fields with frobenian conditions
Mathematika, Volume 72, Issue 4, October 2026.Abstract We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular, we find an asymptotic for the number of abelian field extensions of a number field k$k$ whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.
Julie Tavernier
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Rainbow Connection Number of Dense Graphs
Discussiones Mathematicae Graph Theory, 2013 An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to ...
Li Xueliang +2 more
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Zeros of polynomials in derivatives of automorphic L$L$‐functions
Mathematika, Volume 72, Issue 4, October 2026.Abstract Let Fm$\mathfrak {F}_m$ be the set of all cuspidal automorphic representations of GLm(AQ)$\mathrm{GL}_m(\mathbb {A}_{\mathbb {Q}})$, and let F(s,π)$F(s,\bm {\pi })$ be a polynomial in the derivatives of L$L$‐functions associated with representations π∈⋃m=1∞Fm$\pi \in \bigcup _{m=1}^{\infty } \mathfrak {F}_m$. We establish an asymptotic formula
Anji Dong +2 more
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Australas. J Comb., 2020 JENGA, a very popular game of physical skill, when played by perfect players, can be seen as a pure combinatorial ruleset. Taking that into account, it is possible to play with more than one tower; a move is made by choosing one of the towers, removing a block from there, that is, a disjunctive sum.
Carvalho, Alda +2 more
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Bounded diameter monochromatic component covers
Mathematika, Volume 72, Issue 4, October 2026.Abstract Ryser conjectured that every r$r$‐edge‐coloured complete graph can be covered by r−1$r-1$ monochromatic trees. Motivated by a question of Austin in analysis, Milićević predicted something stronger — that every r$r$‐edge‐coloured complete graph can be covered by r−1$r-1$ monochromatic trees of bounded diameter.
Alexey Pokrovskiy
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