相关论文: Synchronization and separation in the Johnson sche…

The Strong Exponential Time Hypothesis (SETH) is a standard assumption in (fine-grained) parameterized complexity and many tight lower bounds are based on it. We consider a number of reasonable weakenings of the SETH, with sources from (i)…

We show explicitly that the perturbative SU(N) Chern-Simons theory arises naturally from two Penner models, with opposite coupling constants. As a result computations in the perturbative Chern-Simons theory are carried out using the Penner…

Generalizing the notion of a vexillary permutation, we introduce a filtration of S_infinity by the number of Schur function terms in the Stanley symmetric function, with the kth filtration level called the k-vexillary permutations. We show…

A Steiner quadruple system (briefly $SQS(n)$) is a pair $(X,B)$ where $|X|=n$ and $B$ is a collection of 4-element blocks such that every 3-subset of $X$ is contained in exactly one member of $B$. Hanani \cite{Hanani} proved that the…

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously…

Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The…

Let $n$ be a positive integer, $\sigma$ be an element of the symmetric group $\mathcal{S}_n$ and let $\sigma$ be a cycle of length $n$. The elements $\alpha ,\beta \in \mathcal{S}_n$ are $\sigma$-equivalent, if there are natural numbers $k$…

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…

Let $i(\infty,k)$ be the limiting proportion, as $n \rightarrow \infty$, of permutations in the symmetric group of degree $n$ that fix a $k$-set. We give an algorithm for computing $i(\infty,k)$ and state the values of $i(\infty,k)$ for $k…

It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the…

The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…

We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that…

A central theorem in combinatorics is Sperner's Theorem, which determines the maximum size of a family $\mathcal{F}\subseteq \mathcal{P}(n)$ that does not contain a $2$-chain $F_1\subsetneq F_2$. Erd\H{o}s later extended this result and…

We construct a statistic-swapping involution on the Cartesian product of the generalized symmetric group $S(k,n)$ with the symmetric group $S_{kn}$, which swaps the number of fixed points in the generalized symmetric group element with the…

Reasonable requirements of (a) physical invariance under particle permutation and (b) physical completeness of state descriptions, enable us to deduce a Symmetric Permutation Rule(SPR): that by taking care with our state descriptions, it is…

We propose an interpretation for the meets and joins in the lattice of experimental propositions of a physical theory, answering a question of Birkhoff and von Neumann in [1]. When the lattice is atomistic, it is isomorphic to the lattice…

We consider a system of q diffusing particle species A_1,A_2,...,A_q that are all equivalent under a symmetry operation. Pairs of particles may annihilate according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the symmetry, and…

We present a simple theory accounting for two central observations in a recent experiment on quantum coarsening and collective dynamics on a programmable quantum simulator [T. Manovitz et al., Nature \textbf{638}, 86 (2025)]: an apparent…

We show it is possible to obtain quantum pseudorandomness and pseudoentanglement from random subset states -- i.e. quantum states which are equal superpositions over (pseudo)random subsets of strings. This answers an open question of…

We consider a large family of equivalence relations on permutations in Sn that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one…