Results 51 to 60 of about 1,269,170 (176)
Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers
Journal of Mathematics, 2023 In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
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Chromatic Spectrum of $K_s$-WORM Colorings of $K_n$ [PDF]
Computer Science Journal of Moldova, 2020 An {\it $H$-WORM} coloring of a simple graph $G$ is the coloring of the vertices of $G$ such that no copy of $H\subseteq G$ is monochrome or rainbow. In a recently published article by one of the authors \cite{All1}, it was claimed that the number of $r$
Julian A.D. Allagan, Kenneth L. Jones
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$q,t$-Fuß-Catalan numbers for complex reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In type $A$, the $q,t$-Fuß-Catalan numbers $\mathrm{Cat}_n^{(m)}(q,t)$ can be defined as a bigraded Hilbert series of a module associated to the symmetric group $\mathcal{S}_n$.
Christian Stump
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Modular Fuss-Catalan numbers [PDF]
Discrete Mathematics, 2022 The modular Catalan numbers $C_{k,n}$, introduced by Hein and Huang in 2016 count equivalence classes of parenthesizations of $x_0 * x_1 * \dots *x_n$ where $*$ is a binary $k$-associative operation and $k$ is a positive integer. The classical notion of associativity is just 1-associativity, in which case $C_{1,n} = 1$ and the size of the unique class ...
openaire +5 more sources
Some combinatorial identities containing central binomial coefficients or Catalan numbers*
Applied Mathematics in Science and Engineering, 2023 In the article, by virtue of Maclaurin's expansions of the arcsine function and its square and cubic, the authors give a short proof of a sum formula of a Maclaurin's series with coefficients containing reciprocals of the Catalan numbers; establish four ...
Feng Qi, Da-Wei Niu, Dongkyu Lim
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Delannoy numbers and Legendre polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We construct an $n$-dimensional polytope whose boundary complex is compressed and whose face numbers for any pulling triangulation are the coefficients of the powers of $(x-1)/2$ in the $n$-th Legendre polynomial.
Gábor Hetyei
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Permutations avoiding an increasing number of length-increasing forbidden subsequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2000 A permutation π is said to be τ -avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ . This paper concerns the characterization and enumeration of permutations which avoid a set F^j of subsequences increasing ...
Elena Barcucci +3 more
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On Some Properties of Bihyperbolic Numbers of The Lucas Type
Communications in Advanced Mathematical Sciences, 2023 To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
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Bijections between noncrossing and nonnesting partitions for classical reflection groups [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We present $\textit{type preserving}$ bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types $B$, $C$ and $D$ are new in
Alex Fink, Benjamin Iriarte Giraldo
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