Related papers: On the likelihood of normalisation in combinatory …
A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special…
For a nonnegative integer $t$, let $c_t$ be the asymptotic density of natural numbers $n$ for which $s(n + t) \geq s(n)$, where $s(n)$ denotes the sum of digits of $n$ in base $2$. We prove that $c_t > 1/2$ for $t$ in a set of asymptotic…
We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the…
It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
We study the average-case hardness of establishing that a graph does not have a large clique in both proof and communication complexity. We show exponential lower bounds on the length of cutting planes and bounded-depth resolution over…
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily…
We estimate the asymptotic density of the set $\bar{A}$ of primes $p$ satisfying the constraint that $p+1$ and $p-1$ have only one prime divisor larger than $3$. We also estimate the density of a maximal subset $\bar{B} \subset \bar{A}$…
We prove a collection of asymptotic density results for several interesting classes of the $I$-graphs. Specifically, we quantify precisely the proportion of $I$-graphs that are generalised Petersen graphs as well as those that are…
I give a proof of the confluence of combinatory strong reduction that does not use the one of lambda-calculus. I also give simple and direct proofs of a standardization theorem for this reduction and the strong normalization of simply typed…
We study the asymptotic expansion of the determinant of the graph Laplacian associated to discretizations of a half-translation surface endowed with a flat unitary vector bundle. By doing so, over the discretizations, we relate the…
We investigate asymptotic behaviour of probabilities of large deviations for normalized combinatorial sums. We find a zone in which these probabilities are equivalent to the tail of the standard normal law. Our conditions are similar to the…
We study binomially weighted summation methods given by \[ (x_n)_{n\in \mathbb{N}} \mapsto \left(\sum_{k=0}^n\binom{n}{k}r^k(1-r)^{n-k}x_k\right)_{n\in \mathbb{N}} \] for $r\in (0,1)$, and their behavior under composition with summation…
A relaxed $k$-ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree $k$. These objects arise in the compression of trees in which some repeated subtrees are factored and repeated…
Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of…
We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these…