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Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 8
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2011, Volume 434, Issue 3, pp. 712 - 722
We use combinatorial methods to evaluate Hankel determinants for the sequence of sums of consecutive t-Motzkin numbers. More specifically, we consider the... 
Combinatorial proofs | Nonintersecting lattice paths | Chebychev polynomials | Motzkin numbers | Hankel determinants | MATHEMATICS, APPLIED | PATHS | GENERALIZED CATALAN NUMBERS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2005, Volume 305, Issue 1, pp. 170 - 189
We say that a permutation π is a Motzkin permutation if it avoids 132 and there do not exist a < b such that π a < π b < π b + 1 . We study the distribution of... 
Motzkin path | Restricted permutation | Motzkin permutation | Generalized pattern | Permutation statistic | Chebyshev polynomial | generalized pattern | MATHEMATICS | NUMBER | restricted permutation | AVOIDANCE | GENERALIZED PATTERNS | FORBIDDEN SUBSEQUENCES | permutation statistic
Journal Article
Journal of Number Theory, ISSN 0022-314X, 06/2019, Volume 199, pp. 389 - 402
We study the higher-order Euler polynomials and give the corresponding monic orthogonal polynomials, which are the Meixner–Pollaczek polynomials with certain... 
Generalized Motzkin number | Higher-order Euler polynomials | Orthogonal polynomial | Meixner–Pollaczek polynomial | MATHEMATICS | BERNOULLI | Meixner-Pollaczek polynomial
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 05/2019, Volume 106, pp. 1 - 19
In this paper, we study pattern avoidances of generalized permutations and show that the number of all generalized permutations avoiding π is independent of... 
Pattern avoidances | RSK correspondence | Generalized permutations | Motzkin numbers | Riordan numbers | Young tableaux | MATHEMATICS, APPLIED
Journal Article
Journal of Integer Sequences, 01/2015, Volume 18, Issue 2
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 7/2018, Volume 34, Issue 7, pp. 1101 - 1109
We show that many well-known counting coefficients in combinatorics are Hamburger moment sequences in certain unified approaches and that Hamburger moment... 
Hankel matrix | 05A99 | total positivity | 15B99 | generalized Motzkin number | infinite convexity | Mathematics, general | Hamburger moment sequence | Mathematics | 44A60 | Stieltjes moment sequence | MATHEMATICS | MATHEMATICS, APPLIED | CATALAN-LIKE NUMBERS | Combinatorics | Polynomials | Combinatorial analysis
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 11/2012, Volume 437, Issue 9, pp. 2285 - 2299
We consider weighted large and small Schröder paths with up steps (1,1), down steps (1,-1) assigned the weight of 1 and with level steps (2,0) assigned the... 
Non-intersecting lattice paths | Schröder numbers | Combinatorial methods | Hankel determinants | MATHEMATICS | MATHEMATICS, APPLIED | MOTZKIN NUMBERS | Lattice paths | PATHS | Schroder numbers | GENERALIZED CATALAN NUMBERS
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 12, pp. 3936 - 3953
We consider sequences of polynomials which count lattice paths by area. In some cases the reversed polynomials approach a formal power series as the length of... 
Motzkin paths | Schröder paths | Generalized Frobenius partitions | Schroder paths | MATHEMATICS | NUMBERS
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 7/2005, Volume 9, Issue 2, pp. 137 - 162
We settle some conjectures formulated by A. Claesson and T. Mansour concerning generalized pattern avoidance of permutations. In particular, we solve the... 
generalized patterns avoidance | succession rules | Fibonacci and Motzkin numbers | Mathematics | Combinatorics | 05A05 | permutations | 05A15 | Generalized patterns avoidance | Permutations | Succession rules | MATHEMATICS, APPLIED
Journal Article
Ars Combinatoria, ISSN 0381-7032, 01/2016, Volume 125, pp. 225 - 246
Bizley [J. Inst. Actuar. 80 (1954), 55-62] studied a generalization of Dyck paths from (0, 0) to (pn, qn) (gcd(p, q) = 1), which never go below the line py =... 
Lattice paths | 05A19 | Generating functions. 2010 Mathematics Subject Classification: 05A15 | Generalized Dyck paths | 11B83 | Motzkin numbers | MATHEMATICS | lattice paths | generating functions | generalized Dyck paths
Journal Article
Acta Informatica, ISSN 0001-5903, 4/2006, Volume 42, Issue 8, pp. 603 - 616
We consider in this paper the class M k n of generalized Motzkin paths of length n, that is, lattice paths using steps (1,1), (1,−1), (k,0), where k is a fixed... 
Rejection | Generalized Motzkin path | Random generation | COMPUTER SCIENCE, INFORMATION SYSTEMS | generalized Motzkin path | random generation | AREA | rejection | Studies | Algorithms | Integers | Origins | Lattices | Running | Complexity
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 4/2017, Volume 173, Issue 1, pp. 131 - 154
Journal Article
Journal of the Operational Research Society, ISSN 0160-5682, 07/2017, Volume 68, Issue 7, pp. 829 - 833
The Dependency Diagram of a Linear Programme (LP) shows how the successive inequalities of an LP depend on former inequalities, when variables are projected... 
generalised Chinese remainder theorem | elimination of variables | linear congruences | projection | integer programming | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | Integer programming | Analysis | Polytopes | Mixed integer | Linear programming | Congruences | Inequalities
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 08/2002, Volume 6, Issue 1, pp. 65 - 76
Recently, Babson and Steingrimsson (see [2]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern... 
restricted permutations, generalized patterns, Chebyshev polynomials
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 02/2017, Volume 146, pp. 312 - 343
The family Σr consists of all r-graphs with three edges D1,D2,D3 such that |D1∩D2|=r−1 and D1△D2⊆D3. A generalized triangle, Tr∈Σr is an r-graph on... 
Turán number | Symmetrization | Stability | Weighted hypergraphs | Steiner systems | Generalized triangle | Blowups | Lagrangian function | THEOREM | HYPERGRAPHS | GRAPHS | MATHEMATICS | REGULARITY | Turan number
Journal Article
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