23 papers · ranked by Valyu relevance
Duaa Abdullah, Jasem Hamoud
This paper begins with a comprehensive overview of combinatorics on words and symbolic dynamics, covering their historical origins, fundamental concepts, and interconnections. Building upon this foundation, we introduce novel mathematical constructions related to pattern avoidance in infinite words. Specifically, we…
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…
Michael A. Allen
We consider the restricted subsets of Nn = {1, 2, . . . , n} with q ≥ 1 being the largest member of the set Q of disallowed differences between subset elements. We obtain new results on various classes of problem involving such combinations lacking specified separations. In particular, we find recursion relations for…
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…
Ali Kemal Uncu
We present new proofs of two identities arising in work of Mourad Ismail using partition theoretic generating function interpretations.
Raul Penaguiao
In this paper, we expand on the notion of combinatorial presheaf, first introduced explicitly by Aguiar and Mahajan in 2010 but already present in the literature in some other points of view. We do this by adapting the algebraic framework of species to the study of substructures in combinatorics. Afterwards, we…
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…
Hopkins, Brian
There are three long-known types of restricted integer compositions whose counts match the Fibonacci sequence: one from ancient India and two from 19th century England. We give proofs of these enumeration results using tiling arguments and discuss how these can be used in combinatorial proofs of several Fibonacci…
Zile Hui
This work establishes a definition that is more basic than the previous ones, for the Stirling numbers of first kind, which is a sufficient but not necessary condition for the previous definition. Based on this definition and a combinatorial problem, we discover C sequential optimization numbers, where C is a k+1-tuple…
Florian Schreier-Aigner
We introduce a symmetry class for higher dimensional partitions-fully complementary higher dimensional partitions (FCPs)-and prove a formula for their generating function. By studying symmetry classes of FCPs in dimension 2, we define variations of the classical symmetry classes for plane partitions. As a by-product…
Matthew C. King, Noah A. Rosenberg
How many ways are there to arrange the sequence of games in a single-elimination sports tournament? We consider the connection between this enumeration problem and the enumeration of “labeled histories,” or sequences of asynchronous branching events, in mathematical phylogenetics. The possibility of playing multiple…
Rineau Valentin, Prin Stéphane
Triplets, as minimal informative rooted trees, are fundamental units of information in phylogenetics. Their importance for phylogenetic reconstruction, cladistic biogeography, or supertree methods relies on the fact that any rooted tree can be decomposed into a set of triplets. In order to formalize the tree building…
Atli Fannar Franklín, Anders Claesson, Christian Bean, Henning Úlfarsson + 1 more
'Henning Úlfarsson' 'Jay Pantone'] Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion and Schmidt [6], we investigate all…
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…
Atli Fannar Franklín
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion and Schmidt, we investigate all combinations of permutation patterns of length…
Adriano R. Lameira, Madeleine E. Hardus, Andrea Ravignani, Teresa Raimondi + 1 more
Recursive procedures that allow placing a vocal signal inside another of similar kind provide a neuro-computational blueprint for syntax and phonology in spoken language and human song. There are, however, no known vocal patterns among nonhuman primates arranged in self-embedded combinations that evince vocal recursion…
Sophie Hertel, Richard E. Spinney, Stephanie Y. Xu, Thomas E. Ouldridge + 2 more
The kinetics of DNA hybridisation are fundamental to biological processes and DNA-based technologies. However, the precise physical mechanisms that determine why different DNA sequences hybridise at different rates are not well understood. Secondary structure is one predictable factor that influences hybridisation…
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…
Shaili Mathur, Noah A. Rosenberg
Objective In mathematical phylogenetics, a labeled rooted binary tree topology can possess any of a number of labeled histories, each of which represents a possible temporal ordering of its coalescences. Labeled histories appear frequently in calculations that describe the combinatorics of phylogenetic trees. Here, we…
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…