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Rational noncrossing Coxeter–Catalan combinatorics
Proceedings of the London Mathematical Society, 2022We solve two open problems in Coxeter–Catalan combinatorics. First, we introduce a family of rational noncrossing objects for any finite Coxeter group, using the combinatorics of distinguished subwords.
Pavel Galashin +3 more
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Coincidences of Catalan and q-Catalan Numbers
Integers, 2011AbstractLet
Paul Thomas Young, Florian Luca
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Letters of a given size in Catalan words
Discrete Mathematics LettersA Catalan word with n letters, w = w 1 w 2 . . . w n over the set of positive integers is a word in which w 1 = 1 and for each i ∈ { 2 , 3 . . . , n } , the inequality w i ≤ w i − 1 + 1 holds.
A. Blecher, A. Knopfmacher
semanticscholar +1 more source
2015
The most important special case of Dyck words comes when \( a=b \) so that the words have the same number of dominant and nondominant letters. A slight variation on these Dyck words is ballot , which we also define here for completeness.
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The most important special case of Dyck words comes when \( a=b \) so that the words have the same number of dominant and nondominant letters. A slight variation on these Dyck words is ballot , which we also define here for completeness.
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Selected Chapters of Number Theory: Special Numbers
Suppose you have n pairs of parentheses and you would like to form valid groupings of them, where “valid” means that each open parenthesis has a matching closed parenthesis. For example, “(()())” is valid, but “())()(” is not.
Elena Deza
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Suppose you have n pairs of parentheses and you would like to form valid groupings of them, where “valid” means that each open parenthesis has a matching closed parenthesis. For example, “(()())” is valid, but “())()(” is not.
Elena Deza
semanticscholar +1 more source
Revista Colombiana de Ciencias Químico Farmacéuticas
Introduction: Solubility is one of the most basic information in a re-crystallization process and in many cases, there are only a few grams (or even mg or mg) of an expensive pharmaceutical or fine chemical to make a large number of crystallization tests.
Soma Khezri, Parisa Jafari, A. Jouyban
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Introduction: Solubility is one of the most basic information in a re-crystallization process and in many cases, there are only a few grams (or even mg or mg) of an expensive pharmaceutical or fine chemical to make a large number of crystallization tests.
Soma Khezri, Parisa Jafari, A. Jouyban
semanticscholar +1 more source
Catalan Numbers and Permutations
2015We turn now to a vast subject called that is currently the subject of much research. Let S n denote the set of all permutations of [n].
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Catalan Numbers and Semiorders
2015(The Appendix of this book contains a brief introduction to the subject of partial orders for those who are interested.)
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2019
The Fibonacci numbers are pretty cool, but in modern algebraic combinatorics, the most interesting sequence is the sequence of Catalan numbers: $$\begin{aligned} 1, 1, 2, 5, 14, 42, 132, 429,\ldots \end{aligned}$$ The remarkable ability of these numbers to pop up in surprising locations has led some to joke that a combinatorics paper is not ...
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The Fibonacci numbers are pretty cool, but in modern algebraic combinatorics, the most interesting sequence is the sequence of Catalan numbers: $$\begin{aligned} 1, 1, 2, 5, 14, 42, 132, 429,\ldots \end{aligned}$$ The remarkable ability of these numbers to pop up in surprising locations has led some to joke that a combinatorics paper is not ...
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Bidirectionality of language contact: Spanish and Catalan vowels
Proceedings of the Linguistic Society of America, 2021Annie Helms
exaly