| 1. |
- Bränden, Petter, 1976-, et al.
(författare)
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Lower bounds for contingency tables via Lorentzian polynomials
- 2023
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Ingår i: Israel Journal of Mathematics. - : Springer Nature. - 0021-2172 .- 1565-8511. ; 253:1, s. 43-90
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Tidskriftsartikel (refereegranskat)abstract
- We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok [Bar09, Bar16] and Gurvits [Gur15]. As an application, we obtain new lower bounds on the volumes of flow and transportation polytopes. Our proofs are based on recent results on Lorentzian polynomials.
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| 2. |
- Damjanović, Danijela, et al.
(författare)
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On classification of higher rank Anosov actions on compact manifold
- 2020
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Ingår i: Israel Journal of Mathematics. - : Springer Nature. - 0021-2172 .- 1565-8511. ; 238:2, s. 745-806
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Tidskriftsartikel (refereegranskat)abstract
- We prove global smooth classification results for Anosov ℤk actions on general compact manifolds, under certain irreduciblity conditions and the presence of sufficiently many Anosov elements. In particular, we remove all the uniform control assumptions which were used in all the previous results towards the Katok-Spatzier global rigidity conjecture on general manifolds. The main idea is to create a new mechanism labelled nonuniform redefining argument, to prove continuity of certain dynamically-defined objects. This leads to uniform control for higher-rank actions and should apply to more general rigidity problems in dynamical systems.
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| 3. |
- Dao, Hailong, et al.
(författare)
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On generalized Hilbert–Kunz function and multiplicity
- 2020
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 237:1, s. 155-184
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Tidskriftsartikel (refereegranskat)abstract
- Let (R, m) be a local ring of characteristic p > 0 and M a finitely generated R-module. In this note we consider the limitwhere F(-) is the Peskine-Szpiro functor. A consequence of our main results shows that the limit always exists when R is excellent, equidimensional and has an isolated singularity. Furthermore, if R is a complete intersection, then the limit is 0 if and only if the projective dimension of M is less than the Krull dimension of R. We exploit this fact to give a quick proof that if R is a complete intersection of dimension 3, then the Picard group of the punctured spectrum of R is torsion-free. Our results work quite generally for other homological functors and can be used to prove that certain limits recently studied by Brenner exist over projective varieties.
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| 4. |
- Dostert, Maria, et al.
(författare)
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Semidefinite programming bounds for the average kissing number
- 2022
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Ingår i: Israel Journal of Mathematics. - : Springer Nature. - 0021-2172 .- 1565-8511. ; 247:2, s. 635-659
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Tidskriftsartikel (refereegranskat)abstract
- The average kissing number in ℝn is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in ℝn. We provide an upper bound for the average kissing number based on semidefinite programming that improves previous bounds in dimensions 3,.., 9. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions 6,.., 9 our new bound is the first to improve on this simple upper bound.
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| 5. |
- Narayanan, Sridhar, et al.
(författare)
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The multiset partition algebra
- 2023
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Ingår i: Israel Journal of Mathematics. - : Springer Nature. - 0021-2172 .- 1565-8511. ; 255:1, s. 453-500
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the multiset partition algebra MPk(ξ) over the polynomial ring F[ξ], where F is a field of characteristic 0 and k is a positive integer. When ξ is specialized to a positive integer n, we establish the Schur—Weyl duality between the actions of resulting algebra MPk(n) and the symmetric group Sn on Symk(Fn). The construction of MPk(ξ) generalizes to any vector λ of non-negative integers yielding the algebra MPλ(ξ) over F[ξ] so that there is Schur—Weyl duality between the actions of MPλ(n) and Sn on Symλ(Fn). We find the generating function for the multiplicity of each irreducible representation of Sn in Symλ(Fn), as λ varies, in terms of a plethysm of Schur functions. As consequences we obtain an indexing set for the irreducible representations of MPk(n) and the generating function for the multiplicity of an irreducible polynomial representation of GLn(F) when restricted to Sn. We show that MPλ(ξ) embeds inside the partition algebra P|λ|(ξ). Using this embedding, we show that the multiset partition algebras are generically semisimple over F. Also, for the specialization of ξ at v in F, we prove that MPλ(v) is a cellular algebra.
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| 6. |
- Wang, Mengdi
(författare)
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Waring–Goldbach problem in short intervals
- 2023
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Ingår i: Israel Journal of Mathematics. - : Springer Nature. - 0021-2172 .- 1565-8511.
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Tidskriftsartikel (refereegranskat)abstract
- Let k ≥ 2 and s be positive integers. Let θ ∈ (0, 1) be a real number. In this paper, we establish that if s > k(k + 1) and θ > 0.55, then every sufficiently large natural number n, subject to certain congruence conditions, can be written as n=p1k+⋯+psk, , where pi (1 ≤ i ≤ s) are primes in the interval ((ns)1k−nθk,(ns)1k+nθk] . The second result of this paper is to show that if s>k(k+1)2 and θ > 0.55, then almost all integers n, subject to certain congruence conditions, have the above representation.
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| 7. |
- Xia, Mingchen, 1994
(författare)
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On Liu morphisms in non-Archimedean geometry
- 2023
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 1565-8511 .- 0021-2172. ; 255:2, s. 821-850
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Tidskriftsartikel (refereegranskat)abstract
- We define Liu morphisms and quasi-Liu morphisms between Berkovich analytic spaces. We show that Liu morphisms and quasi-Liu morphisms behave exactly as affine morphisms and quasi-affine morphisms of schemes.
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