相关论文: The Sunflower-Free Process

Consider a number, finite or not, of urns each with fixed capacity $r$ and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain $r$ balls. When $r=1$, using analytic…

A well-known problem in numerical ecology is how to recombine presence-absence matrices without altering row and column totals. A few solutions have been proposed, but all of them present some issues in terms of statistical robustness (i.e.…

We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

This paper questions the generally accepted assumption that one can make a random choice that is independent of the rest of the universe. We give a general description of any setup that could be conceived to generate random numbers. Based…

Let $\mathcal{R}$ be an association scheme with nontrivial relations $A_1,\ldots,A_d$. We call $\mathcal{R}$ amorphic if every possible fusion of its nontrivial relations gives rise to a fusion scheme. We define the fusing-relations…

We formulate a statistical-mechanical description of a recently introduced random planting model in which plants are represented by growing hard disks. Seedlings of negligible size are introduced at random positions in a field, grow at a…

We consider a generalisation of the classical coupon collector problem. We define a super-coupon to be any $s$-subset of a universe of $n$ coupons. In each round, a random $r$-subset from the universe is drawn and all its $s$-subsets are…

Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…

We present some problems and results about variants of sunflowers in families of sets. In particular, we improve an upper bound of the first author, K\"orner and Monti on the maximum number of binary vectors of length $n$ so that every four…

The flower at a point x in a Steiner triple system (X; B) is the set of all triples containing x. Denote by J3F(r) the set of all integers k such that there exists a collection of three STS(2r+1) mutually intersecting in the same set of k +…

We study coverage processes in which each draw reveals a subset of $[n]$, and the goal is to determine the expected number of draws until all items are seen at least once. A classical example is the Coupon Collector's Problem, where each…

Let $C_n$ be a cyclic group of order $n$. A sequence $S$ of length $\ell$ over $C_n$ is a sequence $S = a_1\boldsymbol\cdot a_2\boldsymbol\cdot \ldots\boldsymbol\cdot a_{\ell}$ of $\ell$ elements in $C_n$, where a repetition of elements is…

This review of the rapid-neutron-capture (i.e. r-) process starts with determining the Solar System r-abundance pattern via first obtaining (and subtracting) the contribution from the slow-neutron capture (s-) process. We emphasize the…

We consider a simple model of a growing cluster of points in $\Re^d,d\geq 2$. Beginning with a point $X_1$ located at the origin, we generate a random sequence of points $X_1,X_2,\ldots,X_i,\ldots,$. To generate $X_{i},i\geq 2$ we choose a…

For a fixed integer $r\geqslant 3$, let $\mathbb{H}_r(n,p)$ be a random $r$-uniform hypergraph on the vertex set $[n]$, where each $r$-set is an edge randomly and independently with probability $p$. The random $r$-generalized triadic…

An $(r,w;d)$ cover-free family $(CFF)$ is a family of subsets of a finite set such that the intersection of any $r$ members of the family contains at least $d$ elements that are not in the union of any other $w$ members. The minimum number…

We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…

Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. When such a sequence can be…

We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of…