相关论文: A unifying generalization of Sperner's theorem

The existence of Steiner triple systems STS(n) of order n containing no nontrivial subsystem is well known for every admissible n. We generalize this result in two ways. First we define the expander property of 3-uniform hypergraphs and…

A well-known result of Stanley from 1980 implies that the weak order on a maximal parabolic quotient of the symmetric group $S_n$ has the Sperner property; this same property was recently established for the weak order on all of $S_n$ by…

In "All p-adic reductive groups are tame" Bernstein proved that for a reductive group G over a local non-archimedean field F and a compact open subgroup K of G there exists a uniform bound N(G,K) such that for every irreducible, smooth, and…

We develop a general universality technique for establishing metric scaling limits of critical random discrete structures exhibiting mean-field behavior that requires four ingredients: (i) from the barely subcritical regime to the critical…

The purpose of this note is to revisit the proof of the Gearhardt-Pr\"uss-Hwang-Greiner theorem for a semigroup S(t), following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on the norm…

We prove an abstract compactness theorem for a family of generalized Seiberg-Witten equations in dimension three. This result recovers Taubes' compactness theorem for stable flat $\mathbf{P}\mathrm{SL}_2(\mathbf{C})$-connections as well as…

One of the drawbacks of conventional grand unification scenarios has been that the unification scale is too high to permit direct exploration. In this paper, we show that the unification scale can be significantly lowered (perhaps even to…

In grand unified theories with gauge groups larger than SU(5), the multiplets that contain the known quarks and leptons also contain fermions that are singlets under the Standard Model gauge group. Some of these could be the dark matter of…

We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g. the Griesmer bound, the Johnson bound or the…

Barbieri and Hall have argued that threshold effects at the scale of grand-unification wipe out predictions on the SUSY scale, M_S. Using triviality arguments we give upper bounds on ultraheavy particles, while proton stability gives lower…

Grand Unified Theories (GUTs) based on groups like $SO(10)$ and $SU(5)$ unify Standard Model (SM) fermions into irreducible representations (irreps), and predict additional scalar fields beyond the SM Higgs. In $SO(10)$ GUTs, the scalar…

The Boolean lattice $2^{[n]}$ is the family of all subsets of $[n]=\{1,\dots,n\}$ ordered by inclusion, and a chain is a family of pairwise comparable elements of $2^{[n]}$. Let $s=2^{n}/\binom{n}{\lfloor n/2\rfloor}$, which is the average…

We generalize the Stein-Tomas [17] $L^2$-restricition theorem and the uniform Sobolev estimates of Kenig, Ruiz and the second author [11] by allowing critically singular potential. We also obtain Strichartz estimates for Schr\"odinger and…

The interpretation of the apparent unification of gauge couplings within supersymmetric theories depends on uncertainties induced through heavy particle thresholds. While in standard grand unified theories these effects can be estimated…

Let $\mathcal{F}$ be a family of subsets of $[n]$ and $L$ be a subset of $[n]$. We say $\mathcal{F}$ is an $L$-differencing Sperner system if $|A\setminus B|\in L$ for any distinct $A,B\in\mathcal{F}$. Let $p$ be a prime and $q$ be a power…

We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these…

In the framework of the majorization technique, an improved condition is proposed for the semilocal convergence of the Newton method under the mild assumption that the derivative of the involved operator F(x) is continuous. Our starting…

We classify a supersymmetric extension of the Standard Model by discrete symmetries originating from finite modular symmetries $\Gamma_N$. Since all the couplings in supersymmetric theories of finite modular symmetries $\Gamma_N$ are…

We consider random permutations derived by sampling from stick-breaking partitions of the unit interval. The cycle structure of such a permutation can be associated with the path of a decreasing Markov chain on $n$ integers. Under certain…

Let $\mathcal{P}$ be a subset of primes and for each prime $p\in \mathcal{P}$, consider a subset $\mathcal{L}_p$ of $\mathbb{Z}/p\mathbb{Z}$. We provide restriction estimates with integers $\leq N$ sifted by…