Keywords: شماره کاتالان; Riordan matrix; Semi-Riordan matrix; Catalan number; Motzkin number;
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Keywords: شماره کاتالان; Quiddity cycle; Nichols algebra; Weyl groupoid; Frieze pattern; Catalan number;
Keywords: شماره کاتالان; Arithmetical graph; Ballot number; Catalan number; Critical group; Sandpile group; Laplacian;
Keywords: شماره کاتالان; primary; 11D72; 15B48; secondary; 05C50; 05C76; 11D45; 11B83; 05E99; 11D68; 11C20; Arithmetical structures; M-matrices; Edge subdivision; Path; Cycle; Catalan number; Splitting vertices; Merging vertices; Delta-wye transformation; Clique-star transforma
Keywords: شماره کاتالان; Catalan number; parallelogram polyomino; permutation;
Keywords: شماره کاتالان; geometric graph; production matrix; Catalan number; Riordan array;
Keywords: شماره کاتالان; Coxeter group; Symmetric group; 0-Hecke algebra; Reduced word; Weak order; Radius; Catalan number; Hurwitz action
Lattice paths and the q-ballot polynomials
Keywords: شماره کاتالان; primary; 05A15; secondary; 05A19; Lattice paths; Ballot number; Catalan number; Narayana polynomial; Frobenius partition; Generating function; Reflection principle;
Avoiding vincular patterns on alternating words
Keywords: شماره کاتالان; Alternating word; Up-down word; Pattern-avoidance; Narayana number; Catalan number; Stirling number of the second kind; Dyck path;
Combinatorics of a generalized Narayana identity
Keywords: شماره کاتالان; 05A15; 05A18; 05A19Narayana identity; Catalan number; Riordan array; Non-crossing partition
Schröder matrix as inverse of Delannoy matrix
Keywords: شماره کاتالان; 05A05; 05A15; 05A10; 15A09; 15A36; Delannoy number; Pascal matrix; Catalan number; Schröder number; Riordan array;
Inversion polynomials for 321-avoiding permutations
Keywords: شماره کاتالان; Catalan number; Continued fraction; Dyck path; Generating function; Pattern avoidance; Permutation; Inversion number; Major index; Motzkin path; Polyomino; qq-analogue
Asymptotic behavior and the moderate deviation principle for the maximum of a Dyck path
Keywords: شماره کاتالان; Dyck paths; Catalan number; Moderate deviation principle; Brownian excursion
Ballot matrix as Catalan matrix power and related identities
Keywords: شماره کاتالان; Ballot number; Ballot matrix; Catalan number; Catalan matrix; Generalized hypergeometric function; Generating function
Catalan numbers and pattern restricted set partitions
Keywords: شماره کاتالان; Pattern avoidance; Catalan number; Set partition
Permutation patterns and statistics
Keywords: شماره کاتالان; Avoidance; Catalan number; Fibonacci number; Foata bijection; Generating function; Integer partition; Pattern; Permutation; Integer partition; Inversion number; Mahonian pair; Major index; qq-analogue; Statistic
A pair of operator summation formulas and their applications
Keywords: شماره کاتالان; Delta operator; Bernoulli number; Catalan number; Generalized harmonic number; Stirling numbers
Protected points in ordered trees
Keywords: شماره کاتالان; Ordered tree; Protected point; Catalan number; Fine number; Central binomial coefficient; Motzkin numbers; {0,1,2}{0,1,2}-trees
Some identities on the Catalan, Motzkin and Schröder numbers
Keywords: شماره کاتالان; Catalan number; Motzkin number; Schröder number; Riordan group
Parity reversing involutions on plane trees and 2-Motzkin paths
Keywords: شماره کاتالان; 05A15; 05C30; 05C05Plane tree; Dyck path; 2-Motzkin path; Catalan number; Involution
A combinatorial identity with application to Catalan numbers
Keywords: شماره کاتالان; Primary 11B65; secondary, 05A10, 05A19, 11A07, 11B37Binomial coefficient; Combinatorial identity; Catalan number
Reduction of m-regular noncrossing partitions
Keywords: شماره کاتالان; 05A18; 05A15; 92D20; Partition; Noncrossing partition; m-regular partition; RNA secondary structure; Davenport-Schinzel sequence; Narayana number; Catalan number;
A conjectured combinatorial formula for the Hilbert series for diagonal harmonics
Keywords: شماره کاتالان; Catalan number; Parking functions; Labelled trees; Hilbert series;
Generalized triangulations and diagonal-free subsets of stack polyominoes
Keywords: شماره کاتالان; Enumeration; Polygon; Triangulation; Associahedron; Catalan number; Hankel determinant;