Related papers: Water Cells in Compositions of 1s and 2s
We use generating functions to enumerate Arndt compositions, that is, integer compositions where there is a descent between every second pair of parts, starting with the first and second part, and so on. In 2013, J\"org Arndt noted that…
The purpose of this article is to shed new light on the combinatorial structure of Kazhdan-Lusztig cells in infinite Coxeter groups $W$. Our main focus is the set $\D$ of distinguished involutions in $W$, which was introduced by Lusztig in…
Integer compositions restricted by inequalities on certain pairs of parts were first considered by J\"{o}rg Arndt in 2013 and several variations have been studied recently. Here we consider a broad two-parameter generalization that scales…
In this paper, we consider a particular class of Kazhdan-Lusztig cells in the symmetric group $S_n$, the cells containing involutions associated with compositions $\lambda$ of $n$. For certain families of compositions we are able to give an…
The short version of new quantum quantitative Hierarchic theory, general for solids and liquids is presented. Condensed matter is considered as a system of 3D standing waves of different nature: thermal de Broglie waves (waves B), IR…
Integer compositions with certain colored parts were introduced by Andrews in 2007 to address a number-theoretic problem. Integer compositions allowing zero as some parts were introduced by Ouvry and Polychronakos in 2019. We give a…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
In the frame of collective dynamics in water, models built on elementary excitations and long-range electromagnetic interactions in the cell and bulk liquid are presented. Making use of the low effective mass of water coherence domains…
A composition of $n\in\NN$ is an ordered collection of one or more positive integers whose sum is $n$. The number of summands is called the number of parts of the composition. A palindromic composition of $n$ is a composition of $n$ in…
A \Def{composition} of a positive integer $n$ is a $k$-tuple $(\l_1, \l_2, \dots, \l_k) \in \Z_{> 0}^k$ such that $n = \l_1 + \l_2 + \dots + \l_k$. Our goal is to enumerate those compositions whose parts $\l_1, \l_2, \dots, \l_k$ avoid a…
A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of…
Counting the number of isomers of a chemical molecule is one of the formative problems of graph theory. However, recent progress has been slow, and the problem has largely been ignored in modern network science. Here we provide an…
Second-harmonic scattering experiments of water and other bulk molecular liquids have long been assumed to be insensitive to interactions between the molecules. The measured intensity is generally thought to arise from incoherent scattering…
We apply the cell merging method to a model shallow water problem with a permeable boundary. We use a cut cell approach which is more easily and systematically scalable with different shapes of boundaries. The novel cell merging method…
In this paper, we introduce a simple yet effective tabular data watermarking mechanism with statistical guarantees. We show theoretically that the proposed watermark can be effectively detected, while faithfully preserving the data…
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…
Writing is an ancient communication technique dating back at least 30,000 years. While even sophisticated contemporary writing techniques hinge on solid surfaces for engraving or the deposition of ink, writing within a liquid medium…
We discover a surprising connection between Carrollian symmetries and hydrodynamics in the shallow water approximation. Carrollian symmetries arise in the speed of light going to zero limit of relativistic Poincar\'e symmetries. Using a…
Network modelling of water retention and conductivity of porous geomaterials based on filling and emptying of pores requires the use of a computational cell which is a representative volume element of the material. The conditions for the…