Related papers: Some notes on trees and paths
The stable profile of the boundary of a plant's leaf fluctuating in the direction transversal to the leaf's surface is described in the framework of a model called a "surface \`a godets". It is shown that the information on the profile is…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
This short note is an "elementary'' introduction to the conjectural theory of motives.
This note derives asymptotic upper and lower bounds for the number of planted plane trees on $n$ nodes assigned labels from the set $\{1,2,\ldots, k\}$ with the restriction that on any path from the root to a leaf, the labels must strictly…
The family of trees with palindromic characteristic polynomials is characterized. Large families of graphs with this property are found as well.
This paper has been withdrawn by the author; its content is properly cantained in the paper arXiv:0706.4447, entitled "Pure motives, mixed motives and extensions of motives associated to singular surfaces", and submitted on June 29, 2007.
Which conditions ensure that a digraph contains all oriented paths of some given length, or even a all oriented trees of some given size, as a subgraph? One possible condition could be that the host digraph is a tournament of a certain…
In this short note, we revisit Zeilberger's proof of the classical matrix-tree theorem and give a unified concise proof of variants of this theorem, some known and some new.
We introduce a new variation of Tree Encoding with Nested Intervals, find connections with Materialized Path, and suggest a method for moving parts of the hierarchy.
Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.
This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.
A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving…
This paper describes some of the ideas used in the development of our work on small gaps between primes.
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…
Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
A permutation may be represented by a collection of paths in the plane. We consider a natural class of such representations, which we call tangles, in which the paths consist of straight segments at 45 degree angles, and the permutation is…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
We review the paper [arXiv:1905.12783] and discuss some comments about SYK on random unicycle.
Among subgraphs with a fixed number of vertices of the regular square lattice, we prove inequalities that essentially say that those with smaller boundaries have larger numbers of spanning trees and vice-versa. As an application, we relate…