23 papers · ranked by Valyu relevance
Cristian Lenart
This is a survey of recent developments in combinatorics. The goal is to give a big picture of (and related references for) its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including algebraic geometry), topology, probability theory, and…
Francesco Bova, Avi Goldfarb, Roger G. Melko
Despite the scientific and engineering challenges facing the development of quantum computers, considerable progress is being made toward applying the technology to commercial applications. In this article, we discuss the solutions that some companies are already building using quantum hardware. Framing these as…
Margarita Shevtsova, Alexei Kanel-Belov, Mehdi Golafshan
This article introduces a pedagogical method for solving combinatorial problems that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible questions that might obstruct our path to the correct answer and final solution. With this…
Andrea Brini, Antonio Teolis
| 1 | | Introduction | 4 | | --- | --- | --- | --- | | 2 | | Functions between finite sets | 5 | | | 2.1 | Three elementary problems | 5 | | | 2.2 | The occupancy model | 5 | | | 2.3 | The word model | 7 | | | 2.4 | An elementary probalistic application: the birthday problem . . . | 8 | | 3 | | Binomial coefficients |…
Guillaume J. Filion
Seeding heuristics are the most widely used strategies to speed up sequence alignment in bioinformatics. Such strategies are most successful if they are calibrated, so that the speed-versus-accuracy trade-off can be properly tuned. In the widely used case of read mapping, it has been so far impossible to predict the…
Sanpawat Kantabutra, Mehmet Cunkas
In many combinatorial optimization problems we want a particular set of k out of n items with some certain properties (or constraints). These properties may involve the k items. In the worst case a deterministic algorithm must scan n−k items in the set to verify the k items. If we pick a set of k items randomly and…
Nikolaos Konstantinides
The RNA pseudoknot is a conserved secondary structure encountered in a number of ribozymes, which assume a central role in the RNA world hypothesis. However, RNA folding algorithms could not predict pseudoknots until recently. Analytic combinatorics – a newly arisen mathematical field – has introduced a way of…
Zhumagali Shomanov
The formula that will be discussed in this paper has also been discovered by Andrew Sills[1] from Georgia Southern University. In his paper Professor Sills uses Durfee Squares to prove the formula. In my work, as I have mentioned above, I derive the formula from the tree structure of the partition function.
Wolfgang Hornfeck, Kamil Červený, M. I. Aroyo
The number of Wyckoff sequences of a given subdivision complexity is calculated by means of a generating polynomial approach and a dynamic programming approach. The result depends on the choice of space-group symmetry (which is obligatory) and Wyckoff sequence length (which is optional). It also takes into account…
Douglas E. Iannucci
In this expository note, we introduce the reader to compositions of a natural number, e.g., 2 + 1 + 2 + 1 + 7 + 1 is a composition of 14, and 1 + 2 and 2 + 1 are two different compositions of 3. We discuss some simple restricted forms of compositions, e.g., 23 + 17 + 33 is a composition of 73 into three odd parts. We…
Shuo Chen, Qiong Wu, L. Elliot Hong
We consider group-level statistical inference for networks, where outcomes are multivariate edge variables constrained in an adjacency matrix. The graph notation is used to represent a network, where nodes are identical biological units (e.g. brain regions) shared across subjects and edge-variables indicate the…
Valentin Rineau, Stéphane Prin
Three-item statements, as minimal informative rooted binary phylogenetic trees on three items, are the minimal units of cladistic information. Their importance for phylogenetic reconstruction, consensus and supertree methods relies on both (i) the fact that any cladistic tree can always be decomposed into a set of…
Eric Smith, Harrison B. Smith, Jakob Lykke Andersen
We consider problems in the functional analysis and evolution of combinatorial chemical reaction networks as rule-based, or three-level systems. The first level consists of rules, realized here as graph-grammar representations of reaction mechanisms. The second level consists of stoichiometric networks of molecules and…
Zachariah R. Cross, Mark J. Kohler, Matthias Schlesewsky, M. G. Gaskell + 1 more
'M. G. Gaskell' 'Ina Bornkessel-Schlesewsky'] We hypothesize a beneficial influence of sleep on the consolidation of the combinatorial mechanisms underlying incremental sentence comprehension. These predictions are grounded in recent work examining the effect of sleep on the consolidation of linguistic information…
Darren Glass
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum…
Jiao-Lian Zhao, Feng Qi
In the paper, by the Faà di Bruno formula, the authors establish two explicit formulas for the Motzkin numbers, the generalized Motzkin numbers, and the restricted hexagonal numbers.
Mircea Merca
The problem of base changes for the classical symmetric functions has been solved a long time ago and has been incorporated into most computer software packages for symmetric functions. In this paper, we develop a simple recursive formula for the expansion of the augmented monomial symmetric functions into power sum…
Sayle Sigarreta Ricardo, Hugo Adán Cruz Suárez
In this manuscript, we delve into the exploration of the first and second Zagreb connection indices of both polyomino chains and random polyomino chains. Our methodology relies on the utilization of Markov chain theory. Within this framework, the article thoroughly examines precise formulas and investigates extreme…
Authors not listed
Genetic Algorithms are a powerful method to solve optimization problems with complex cost functions over vast search spaces that rely in particular on recombining parts of previous solutions. Crossover operators play a crucial role in this context. Here, we describe a large class of these operators designed for…
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Previously we posited that a systematic and general description of stereoisomerism could be based upon the principles of the polytopal rearrangement model. The most daunting challenge to this end is to comprehensively describe all possible geometries for arbitrary n-coordinate centres, ABn, and for this we have…
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Curried functions provide a systematic way of transforming multi-argument functions into nested singleargument functions. This transformation allows partial application and supports many central principles of functional programming. Their extension, called curried 𝑘-ary functions, naturally generalizes the familiar…
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The concept of aClassical Structure provides a broad mathematical framework, whereas a Hyperstructure arises via the powerset construction, and an 𝑛-Superhyperstructure is obtained by iterating this construction n times [1]. Intuitively, the n-th powerset corresponds to 𝑛 successive applications of the powerset…
Authors not listed
The notion of a Classical Structure provides a broad mathematical framework, while a Hyperstructure emerges through the powerset construction, and an 𝑛-Superhyperstructure is obtained by iterating this process 𝑛 times [1]. Intuitively, the 𝑛-th powerset corresponds to 𝑛 successive applications of the powerset…