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pro vyhledávání: '"$2$–torsion"'
Autor:
Mészáros, András
Let $T_n$ be a $2$-dimensional determinantal hypertree on $n$ vertices. Kahle and Newman conjectured that the $p$-torsion of $H_1(T_n,\mathbb{Z})$ asymptotically follows the Cohen-Lenstra distribution. For $p=2$, we disprove this conjecture by showin
Externí odkaz:
http://arxiv.org/abs/2404.02308
Autor:
Glaudo, Federico, Kravitz, Noah
For a finite multiset $A$ of an abelian group $G$, let $\text{FS}(A)$ denote the multiset of the $2^{|A|}$ subset sums of $A$. It is natural to ask to what extent $A$ can be reconstructed from $\text{FS}(A)$. We fully solve this problem for $2$-torsi
Externí odkaz:
http://arxiv.org/abs/2305.11062
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Autor:
Wang, Zhangjie, Zhang, Shenxing
Let $E: y^2=x(x-a^2)(x+b^2)$ be an elliptic curve with full $2$-torsion group, where $a$ and $b$ are coprime integers and $2(a^2+b^2)$ is a square. Assume that the $2$-Selmer group of $E$ has rank two. We characterize all quadratic twists of $E$ with
Externí odkaz:
http://arxiv.org/abs/2303.05058
Autor:
Swaminathan, Ashvin
We determine the mean number of 2-torsion elements in class groups of cubic orders, when such orders are enumerated by discriminant. Specifically, we prove that when isomorphism classes of totally real (resp., complex) cubic orders are enumerated by
Externí odkaz:
http://arxiv.org/abs/2211.08729
Autor:
Becher, Karim Johannes
It is shown that, over a field of characteristic not $2$, the dimension of an anisotropic quadratic Pfister form of trivial total signature is at most twice the dimension of some central division algebra of exponent $2$. The proof is based on computa
Externí odkaz:
http://arxiv.org/abs/2302.01431
Autor:
Federico Glaudo, Noah Kravitz
Publikováno v:
Discrete Analysis (2024)
A famous conjecture in graph theory, asked by Kelly (1957) and Ulam (1960) and now known as the reconstruction conjecture, states that every graph with $n\geq 3$ vertices is determined up to isomorphism by the multiset of induced subgraphs with $n-1$
Externí odkaz:
https://doaj.org/article/1951d224c21e40f0a85a34fa83036f1f
Autor:
Clay, Matt
We introduce a condition on the monodromy of a free-by-cyclic group, $G_\phi$, called the chain flare condition, that implies that the $L^2$-torsion, $\rho^{(2)}(G_\phi)$, is non-zero. We conjecture that this condition holds whenever the monodromy is
Externí odkaz:
http://arxiv.org/abs/2107.09775
Autor:
Siad, Artane
We study average $2$-torsion in the class group of monogenised fields of odd degree. Bhargava-Hanke-Shankar have recently shown that the average number of non-trivial $2$-torsion elements in the class group of monogenised cubic fields of a fixed sign
Externí odkaz:
http://arxiv.org/abs/2011.08834
Autor:
Koymans, Peter, Pagano, Carlo
Let $K$ be a multiquadratic extension of $\mathbb{Q}$ and let $\text{Cl}^{+}(K)$ be its narrow class group. Recently, the authors \cite{KP} gave a bound for $|\text{Cl}^{+}(K)[2]|$ only in terms of the degree of $K$ and the number of ramifying primes
Externí odkaz:
http://arxiv.org/abs/2009.08399