相关论文: On the typical values of the cross-correlation mea…

Let $F_1=1,F_2=1,\ldots$ be the Fibonacci sequence. Motivated by the identity $\displaystyle\sum_{k=0}^{\infty}\frac{1}{F_{2^k}}=\frac{7-\sqrt{5}}{2}$, Erd\"os and Graham asked whether $\displaystyle\sum_{k=1}^{\infty}\frac{1}{F_{n_k}}$ is…

For a family $\mathcal{F}$ of sets and a disjoint pair $A,B$ we let $\mathcal{F}(A,\overline{B})=\{F\in \mathcal{F}: A\subseteq F, ~B\cap F=\emptyset\}$. The \textbf{$(p,q)$-d\"omd\"od\"om} of a family $\mathcal{F}\subseteq 2^{[n]}$ is…

The OSSS inequality [O'Donnell, Saks, Schramm and Servedio, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05), Pittsburgh (2005)] gives an upper bound for the variance of a function f of independent 0-1 valued random…

Comparator circuits are a natural circuit model for studying bounded fan-out computation whose power sits between nondeterministic branching programs and general circuits. Despite having been studied for nearly three decades, the first…

The Union-Closed Sets Conjecture asks whether every union-closed set family $\mathcal{F}$ has an element contained in half of its sets. In 2022, Nagel posed a generalisation of this problem, suggesting that the $k$th-most popular element in…

A set $A$ $t$-intersects a set $B$ if $A$ and $B$ have at least $t$ common elements. Families $\mathcal{A}_1, \mathcal{A}_2, \dots, \mathcal{A}_k$ of sets are cross-$t$-intersecting if, for every $i$ and $j$ in $\{1, 2, \dots, k\}$ with $i…

We say that a set $A$ $t$-intersects a set $B$ if $A$ and $B$ have at least $t$ common elements. Two families $\mathcal{A}$ and $\mathcal{B}$ of sets are said to be cross-$t$-intersecting if each set in $\mathcal{A}$ $t$-intersects each set…

We study forcing pairs for quasirandom graphs. Chung, Graham, and Wilson initiated the study of families $\\mathcal F$ of graphs with the property that if a large graph $G$ has approximately homomorphism density $p^{e(F)}$ for some fixed…

Graphs serve as efficient tools for visualizing mathematical concepts and their interrelationships. In this paper, focusing on the discrete case with universal set with finite elements, we first introduce the rules and characteristics of…

We apply two variations of the principle of Minimum Cross Entropy (the Kullback information measure) to fit parameterized probability density models to observed data densities. For an array beamforming problem with P incident narrowband…

For an integer $d \geq 2$, a family $\mathcal{F}$ of sets is $\textit{$d$-wise intersecting}$ if for any distinct sets $A_1,A_2,\dots,A_d \in \mathcal{F}$, $A_1 \cap A_2 \cap \dots \cap A_d \neq \emptyset$, and $\textit{non-trivial}$ if…

A probability measure $P_n$ on the symmetric group ${\mathfrak S}_n$ is said to be record-dependent if $P_n(\sigma)$ depends only on the set of records of a permutation $\sigma\in{\mathfrak S}_n$. A sequence $P=(P_n)_{n\in{\mathbb N}}$ of…

The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the new sequence S_{k,n} with initial conditions S_{k,0} = 2b and S_{k,1} = bk + a, which is generated by the…

If a family $\mathcal{F}$ of $k$-element subsets of an $n$-element set is pairwise intersecting, $2k\leq n$ then $|\mathcal{F}|\leq {n-1\choose k-1}$ holds by the celebrated Erd\H{o}s-Ko-Rado theorem. But an intersecting family obviously…

Let $G$ be a countable cancellative amenable semigroup and let $(F_n)$ be a (left) F{\o}lner sequence in $G$. We introduce the notion of an $(F_n)$-normal element of $\{0,1\}^G$. When $G$ = $(\mathbb N,+)$ and $F_n = \{1,2,...,n\}$, the…

Let $(X,\mathcal{B},\mu,T)$ be a measure preserving system. We say that a function $f\in L^2(X,\mu)$ is $\mu$-mean equicontinuous if for any $\epsilon>0$ there is $k\in \mathbb{N}$ and measurable sets ${A_1,A_2,\cdots,A_k}$ with…

Let F be a family of positive homothets (or translates) of a given convex body K in R^n. We investigate two approaches to measuring the complexity of F. First, we find an upper bound on the transversal number $\tau(F)$ of F in terms of $n$…

This paper tells the story how a MAPLE-assisted quest for an interesting undergraduate problem in trigonometric series led some "amateurs" to the discovery that the one-parameter family of deterministic trigonometric series $\pzcS_p:…

In this paper,our main focus is to obtain an asymptotic bound on the family wise error rate (FWER) for Bonferroni-type procedure in the simultaneous hypotheses testing problem when the observations corresponding to individual hypothesis are…

For arrays $(S_{i,j})_{1\leq i\leq j}$ of random variables that are stationary in an appropriate sense, we show that the fluctuations of the process $(S_{1,n})_{n=1}^{\infty}$ can be bounded in terms of a measure of the ``mean…