Keywords: 05A15; 05C50; 05D15; t-Term rank; Interchange; Row sum vector; Column sum vector;
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Keywords: 05A05; 05A15; Permutation patterns; Functional equations; Enumeration algorithm;
Keywords: 05A15; 15A06; 15A15; Rises; Weak-rises; Levels; Descents; Weak-descents; Generating functions; Cramer's method;
Keywords: 05A05; 05A18; 05A15; 05A16; Permutation patterns; Ordered set partitions; Words; Exact enumeration; Asymptotic enumeration;
Keywords: 05A15; 05A40; 11B83; 11C20Determinants; Riordan arrays; Sheffer sequences; Umbral calculus
Keywords: 05A05; 05A10; 05A15; 05A19Trees; Posets; Parallelogram polyominoes; Tree-like tableaux; Bessel function; Permutations excedances
Keywords: primary; 11B75; secondary; 05A15; 05A18; 11A07; Bell polynomials; Derangement polynomials; Stirling numbers; Congruences;
Keywords: 05A18; 05A15; 15A06; 15A09; Set partition; Parity succession; Tridiagonal matrix; Generating function;
Keywords: 62H99; 05A15; 05C90; 62J05; Gaussian graphical model; Conditional independence; Determinant; Lindström-Gessel-Viennot Lemma;
Keywords: 14H55; 20M14; 05A15; Numerical semigroup; Weierstrass semigroup; Genus of numerical semigroup; Frobenius number;
Keywords: primary; 13F25; secondary; 05A15; Formal power series;
Keywords: 05A15; 05A19; 05E10; One-face maps; Constellations; Jacksonʼs formula;
Keywords: 05A15; 13P10; 20M14Numerical semigroup; Apéry set; Frobenius number; Cohen–Macaulay type; Genus; Pseudo-symmetry
Keywords: 05A15; 11T24Subset sums; Quadratic residue; Character sum; Distinct coordinate sieve
Keywords: 05A05; 05A15; 05A20Pattern Avoidance; γ-Positivity; Separable permutations; Descents; Excedances; Inversions
Keywords: 05A15; 05A19Context-free grammar; Eulerian grammar; Grammatical labeling; Increasing tree; Exterior peak of a permutation; Stirling permutation
Keywords: 05A15; 05A19; 05A30; 11B65; 11B73; 11B83Rook numbers; q-Analogues; Elliptic extensions; Alpha-parameter model; Matchings
Keywords: 05A15; 05A30; 11B68; 33B10Entringer numbers; Poupard numbers; Tangent numbers; Secant numbers; Linear refinement; Entringer–Poupard matrix sequence; Matrix refinement; Alternating permutations; Three-variate generating function calculus; Seidel and skew S
Keywords: 05A15; 05C30; 05C70Graphical condensation; Lozenge tilings; Perfect matchings; Plane partitions
Keywords: Lucas sequence; Generalized Lucas sequence; Recurrence relations; Quaternions11B39; 05A15; 11R52
Keywords: 05A15; 05C70Domino tilings; Lozenge tilings; Perfect matchings; Plane partitions; Urban renewal
Keywords: 11T06; 05A15; Finite field; Normal basis; N-polynomial; q-polynomial;
Refinements of two identities on (n,m)-Dyck paths
Keywords: 05A15; Lattice paths; (n,m)-Dyck paths; Peaks; Chung-Feller theorem; Bijective proof;
Elementary proof and application of the generating functions for generalized Hall-Littlewood functions
Keywords: primary; 05E05; secondary; 55N22; 05A15; Hall-Littlewood function; Formal group law; Generating function;
Half of a Riordan array and restricted lattice paths
Keywords: 05A05; 05A15; 05A10; 15A09; 15A36; Riordan array; Lukasiewicz path; Central coefficients; Catalan numbers; Generating function;
Some properties of central Delannoy numbers
Keywords: primary; 11Y55; secondary; 05A15; 05A19; 05A20; 11B75; 11B83; 11Y35; 26A48; 30E20; 33B99; 44A10; 44A15; Central Delannoy number; Explicit expression; Identity; Cauchy product; Integral representation; Monotonicity;
Detecting the integer decomposition property and Ehrhart unimodality in reflexive simplices
Keywords: 52B20; 05E40; 05A20; 05A15;
Ehrhart tensor polynomials
Keywords: 05A10; 05A15; 15A45; 15A69; 52B20; 52B45; Ehrhart tensor polynomial; hr-tensor polynomial; Pick's formula; Positive semidefinite coefficients; Half-open polytopes;
Wilf equivalence relations for consecutive patterns
Keywords: 05A05; 05A15; 06A07; Permutation; Consecutive pattern; c-Wilf equivalence; Super-strong; Poset; Cluster method;
Signed countings of types B and D permutations and t,q-Euler numbers
Keywords: 05A05; 05A15; 05A19; Euler number; Springer number; Signed permutations; Derangements; Continued fractions; Weighted bicolored Motzkin paths;
Edge contraction on dual ribbon graphs and 2D TQFT
Keywords: primary; 14N35; 81T45; 14N10; secondary; 53D37; 05A15; Topological quantum field theory; Frobenius algebras; Ribbon graphs; Cell graphs;
Interactions between interleaving holes in a sea of unit rhombi
Keywords: 05A15; 05A16; 33C20; 52C20; 82B20; Rhombus tilings; Two dimensional electrostatics;
A trinity of duality: Non-separable planar maps, β(1,0)-trees and synchronized intervals
Keywords: 05A15; 05A19; 05C30; Non-separable planar maps; β-(1,0) trees; Synchronized intervals; Bijection; Map duality; Recursive decomposition;
Some determinants of path generating functions, II
Keywords: primary; 05A19; secondary; 05A10; 05A15; 11C20; 15A15; Hankel determinants; Catalan numbers; Ballot numbers; Motzkin numbers; Motzkin prefix numbers; Motzkin paths;
Some explicit and recursive formulas of the large and little Schröder numbers
Keywords: primary; 11Y55; secondary; 05A15; 11B83; 11R33; 26A48; 30E20; 44A10; 44A15; Explicit formula; Recursive formula; Schröder number; Generating function;
Explicit expressions for the moments of the size of an (s,s + 1)-core partition with distinct parts
Keywords: 05A17; 05A15; 05A16; 05E10; Simultaneous core partitions; Automated enumeration; Combinatorial statistics; Asymptotic normality;
A twisted duality for parabolic Kazhdan-Lusztig R-polynomials
Keywords: primary; 20F55; secondary; 05E15; 05A15; Coxeter group; Parabolic R-polynomial; Parabolic Kazhdan-Lusztig polynomial;
Generalized Humbert polynomials via generalized Fibonacci polynomials
Keywords: Generalized (p, q)-Fibonacci polynomials; Generalized (p, q)-Lucas polynomials; Generalized Humbert polynomials; Combinatorial identities; Determinants; 05A15; 05A19; 11B39;
The group of multi-dimensional Riordan arrays
Keywords: 05A15; Riordan group; Multi-dimensional Riordan array; Group extension;
Divisibility properties of the r-Bell numbers and polynomials
Keywords: primary; 11B83; secondary; 11B73; 05A15; 05A19; 05A16; r-Bell numbers; r-Stirling numbers; Touchard's congruence; p-adic valuation;
Identities involving weighted Catalan, Schröder and Motzkin paths
Keywords: primary; 05A15; secondary; 05A10; 05A19; Motzkin numbers; Catalan numbers; Narayana numbers; Schröder numbers; Weighted lattice paths; Bijection;
Lattice paths and the q-ballot polynomials
Keywords: primary; 05A15; secondary; 05A19; Lattice paths; Ballot number; Catalan number; Narayana polynomial; Frobenius partition; Generating function; Reflection principle;
Fuss-Catalan matrices, their weighted sums, and stabilizer subgroups of the Riordan group
Keywords: 05A15; 05A05; 15B36; 15A06; 05A19; 11B83; Riordan group; Generating function; Fundamental theorem of Riordan arrays; Catalan numbers; Fuss-Catalan numbers; Fuss-Catalan matrices; Stabilizer;
Enumerating secondary structures and structural moieties for circular RNAs
Keywords: 05A15; 05A16; 60C05; 92C40; 92E10; Genotype-phenotype map; Analytic combinatorics; Viroids;
Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
Keywords: primary; 05A10; 05A15; 11B37; 11B39; 11B68; 11B83; 11M35; 26C05; 26C10; secondary; 33C05; 34A99; 35A99; Generating functions; Functional equations; Partial differential equations; Hypergeometric functions; Hurwitz-Lerch zeta functions; Apostol-Bernoul
On q-integrals over order polytopes
Keywords: primary; 05A30; secondary; 05A15; 06A07; q-Integral; Order polytope; q-Selberg integral; Reverse plane partition; q-Ehrhart polynomial;
On a new generalization of Fibonacci quaternions
Keywords: Fibonacci sequence; Generalized Fibonacci sequence; Recurrence relations; Quaternions; 11B39; 05A15; 11R52;
Shift operators defined in the Riordan group and their applications
Keywords: 05A15; 05A05; 15B36; 15A06; 05A19; 11B83Riordan arrays; Riordan group; Generating function; Shift matrices; Production matrix; Bell subgroup; Chu–Vandermonde identity; Format Last Theorem; Beal Conjecture; Riordan involutions; Riordan pseudo-involutions
Sorting index and Mahonian–Stirling pairs for labeled forests
Keywords: 05A05; 05A15
Applications of Riordan matrix functions to Bernoulli and Euler polynomials
Keywords: 05A05; 05A15; 15B36; 15A09; 05A30; 05A10; 05A19Riordan array; Riordan group; Pascal matrix; Bernoulli polynomials and numbers; Euler polynomials and numbers; Conjugate Bernoulli and Euler polynomials