Catalan numbers, their generalization, and their uses

From MaRDI portal
Publication:1174258

DOI10.1007/BF03024089zbMath0767.05010MaRDI QIDQ1174258

Jean Pedersen, Hilton, Peter

Publication date: 25 June 1992

Published in: The Mathematical Intelligencer (Search for Journal in Brave)




Related Items

Monotonicity of conditional distributions and growth models on trees.Gevrey regularity and summability of the formal power series solutions of the inhomogeneous generalized Boussinesq equationsGenerating functions for inverted semistandard Young tableaux and generalized ballot numbersSolving symmetric algebraic Riccati equations with high order iterative schemesCongruences with $q$-generalized Catalan numbers and $q$-harmonic numbers;Congruences with q- generalized Catalan Numbers and q-Harmonic NumbersUnnamed ItemDynamics of a new family of iterative processes for quadratic polynomialsThe Raney numbers and \((s,s+1)\)-core partitionsAnalysis of the Bernstein basis functions: an approach to combinatorial sums involving binomial coefficients and Catalan numbersUnnamed ItemUnnamed ItemColored Motzkin Paths of Higher OrderThe unconditional uniqueness for the energy-supercritical NLSUnnamed ItemRaney numbers, threshold sequences and Motzkin-like pathsGeneralized Path Pairs and Fuss-Catalan TrianglesCombinatorics of generalized Bethe equationsEnumeration of noncrossing trees on a circleModular Fuss-Catalan numbersOn two sequences of orthogonal polynomials related to Jordan blocksCombinatoric enumeration of two-dimensional proper arraysUnnamed ItemComputational identities for extensions of some families of special numbers and polynomialsFacets of the generalized cluster complex and regions in the extended Catalan arrangement of type \(A\)New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithmsCool-lex order and \(k\)-ary Catalan structuresChoiceless Ramsey theory of linear ordersDown-step statistics in generalized Dyck pathsA generalization of Catalan numbers\(p^{q}\)-Catalan numbers and squarefree binomial coefficientsInjectively \(k\)-colored rooted forestsOn Klein's icosahedral solution of the quinticSome new binomial sums related to the Catalan triangleMARGIN TRADING THROUGH HYPER TIMELINEFinite size percolation in regular treesEnumeration of generalized Dyck paths based on the height of down-steps modulo \(k\)Parking on supercritical Galton-Watson treesUnnamed ItemA combinatorial analysis for the critical clause treeCluster and virial expansions for the multi-species Tonks gasBest-reply dynamics in large binary-choice anonymous gamesA new relation among Catalan numbersA circular order on edge-coloured trees and RNA \(m\)-diagramsSeveral identities in the Catalan triangleThe \(m\)-Schröder paths and \(m\)-Schröder numbersDynamic speed scaling minimizing expected energy consumption for real-time tasksThe number of coverings in four catalan latticesEnumerations of plane trees with multiple edges and Raney lattice pathsThe Monotonicity and Log-Behaviour of Some Functions Related to the Euler Gamma FunctionSome results on a class of polynomials related to convolutions of the Catalan sequenceOn Sum of Squares Representation of Convex Forms and Generalized Cauchy--Schwarz InequalitiesAn identity of Andrews and a new method for the Riordan array proof of combinatorial identitiesMultivariate Fuss-Catalan numbers2-binary trees: bijections and related issuesPre-derivations and description of non-strongly nilpotent filiform Leibniz algebrasMoments on Catalan numbersThree identities of the Catalan-Qi numbersNew identities in the Catalan triangleSuper ballot numbersHigher-order matching polynomials and \(d\)-orthogonalityRandom generation of DFAsStationary solutions of random differential equations with polynomial nonlinearitiesDeterminants of (generalised) Catalan numbersOn the application of the matrix formalism for the heat kernel to number theoryFirst-crossing and ballot-type results for some nonstationary sequencesUnnamed ItemMoments of combinatorial and Catalan numbersSingle polygon counting on Cayley tree of order 3Unnamed ItemDeterministic random walks on regular treesNon-crossing trees, quadrangular dissections, ternary trees, and duality-preserving bijectionsStaircase tilings and \(k\)-Catalan structuresRaney and CatalanECO:a methodology for the enumeration of combinatorial objectsLogarithmically complete monotonicity of a function related to the Catalan-Qi functionThe classification of non-characteristically nilpotent filiform Leibniz algebrasLogarithmically complete monotonicity of Catalan-Qi function related to Catalan numbersGevrey regularity of the solutions of the inhomogeneous partial differential equations with a polynomial semilinearityGevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficientsA simplicial complex splitting associativitySet-Valued Tableaux & Generalized Catalan NumbersA pseudo-linear time algorithm for the optimal discrete speed minimizing energy consumptionBijections for 2-plane trees and ternary treesOn the spectra of certain graphs arising from finite fieldsBallot matrix as Catalan matrix power and related identitiesA three-player singled out gameA filtration of \((q,t)\)-Catalan numbersGeneralized noncrossing partitions and combinatorics of Coxeter groupsAn enhanced model of a two player singled out gameUnnamed ItemCUNTZ–KRIEGER ALGEBRAS AND A GENERALIZATION OF CATALAN NUMBERSSome properties of the Fuss-Catalan numbersEvaluations of some Euler-Apéry-type seriesErratic Extremism Causes Dynamic Consensus: A New Model for Opinion DynamicsTriple product sums of Catalan triangle numbersMultiplicative functions on the lattice of non-crossing partitions and free convolutionAn algorithmic framework for fixed-cardinality optimization in sparse graphs applied to dense subgraph problemsLattice paths and the \(q\)-ballot polynomialsLattice paths not touching a given boundaryDihedral sieving on cluster complexesGevrey regularity of the solutions of some inhomogeneous semilinear partial differential equations with variable coefficientsAsymptotics for generating functions of the Fuss-Catalan numbersCounting Lattice Walks in the PlaneLogarithms of Catalan generating functions: a combinatorial approachUnnamed Item



Cites Work


This page was built for publication: Catalan numbers, their generalization, and their uses