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Journal of Integer Sequences, 2018, Volume 21, Issue 6
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2019, Volume 371, Issue 3, pp. 2089 - 2107
The family of lattice simplices in \mathbb{R}^n formed by the convex hull of the standard basis vectors together with a weakly decreasing vector of negative... 
Simplex | Weighted projective space | Binomial coefficients | Ehrhart | Eulerian polynomial | Factoradics | Numeral system | Real-rooted | Binary | Symmetric | Unimodal | numeral system | MATHEMATICS | factoradics | binomial coefficients | binary | weighted projective space | unimodal | symmetric | real-rooted | Mathematics | Naturvetenskap | Natural Sciences | Matematik
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 03/2018, Volume 25, Issue 1
In this paper, we give a combinatorial interpretation of the r-Whitney-Eulerian numbers by means of coloured signed permutations. This sequence is a... 
Unimodality | Eulerian number | r-whitney number | r-whitney-eulerian number | Combinatorial identities | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | r-Whitney number | r-Whitney-Eulerian number | unimodality | KIND | R-WHITNEY NUMBERS | combinatorial identities | DOWLING LATTICES
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 05/2019, Volume 106, pp. 57 - 95
The aim of this paper is two-fold. We first prove several new interpretations of a kind of (q,t)-Catalan numbers along with their corresponding γ-expansions... 
Gamma expansions | Pattern avoidance | [formula omitted]-Phenomenon | Catalan numbers | Narayana polynomials | Alternating permutations | (−1)-Phenomenon | MATHEMATICS, APPLIED | PERMUTATIONS | (-1)-Phenomenon | EULERIAN POLYNOMIALS | Combinatorics | Mathematics
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 10/2013, Volume 24, Issue 10, pp. 817 - 830
These numbers are defined as the coefficients of the Euler-Frobenius polynomials which usually are introduced via the rational function expansion n being a... 
Eulerian numbers | Euler-Frobenius polynomials | local central limit expansions | rounding errors | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | JONQUIERE POLYNOMIALS | ROOTS | ZEROS | Studies | Functions (mathematics) | Asymptotic expansions | Theorems | Approximation | Mathematical analysis | Images | Polynomials | Combinatorial analysis
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 10/2019, Volume 13, Issue 2, pp. 378 - 398
In this paper, we study further properties of a recently introduced generalized Eulerian number, denoted by ( ), which reduces to the classical Eulerian number... 
MATHEMATICS | Eulerian number | MATHEMATICS, APPLIED | Euler-Frobenius fraction | r-Whitney-Eulerian number | combinatorial identity
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 370, Issue 2, pp. 486 - 490
In this paper, the spline interpretations of Eulerian numbers and refined Eulerian numbers are presented. Many classical results about Eulerian numbers can... 
Eulerian numbers | Refined Eulerian numbers | Log-concavity | Descent polynomials | B-splines | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 2010, Volume 31, Issue 7, pp. 1689 - 1705
It is well known that the ( − 1 ) -evaluation of the enumerator polynomials of permutations (resp. derangements) by the number of excedances gives rise to... 
MATHEMATICS | PERMUTATIONS | STATISTICS | EULERIAN POLYNOMIALS | RISES | Nesting | Permutations | Tangents | Inversions | Proving | Mathematical models | Statistics | Combinatorial analysis | Combinatorics | Mathematics
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 02/2016, Volume 23, Issue 1
We introduce a new array of type $D$ Eulerian numbers, different from that studied by Brenti, Chow and Hyatt. We find in particular the recurrence relation,... 
Eulerian numbers | Moments of a probability measure | Signed permutations
Journal Article
International Journal of Multiphase Flow, ISSN 0301-9322, 06/2017, Volume 92, pp. 1 - 19
Journal Article
Experimental Mathematics, ISSN 1058-6458, 04/2015, Volume 24, Issue 2, pp. 183 - 195
In this work, the p-adic valuation of Eulerian numbers is explored. A tree whose nodes contain information about the p-adic valuation of these numbers is... 
Eulerian numbers | Secondary 11B75 | p-adic valuation | Primary 11B50 | Bernoulli numbers | regular primes | Wolstenholme primes | MATHEMATICS | STIRLING NUMBERS | FIBONACCI
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 05/2014, Volume 124, Issue 1, pp. 244 - 250
Erman, Smith, and Várilly-Alvarado (2011) showed that the expected number of doubly monic Laurent polynomials f(z)=z−m+a−m+1z−m+1+⋯+an−1zn−1+zn whose first... 
Bernstein's theorem | Eulerian number | Hypersimplex | MATHEMATICS
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2019, Volume 13, Issue 1, pp. 61 - 72
Simsek [Y. Simsek, New families of special numbers for computing negative order Euler numbers and related numbers and polynomials, Appl. Anal. Discrete Math.... 
Integers | Polynomials | Generating function | Coefficients | Recurrence relations | New family | MATHEMATICS | MATHEMATICS, APPLIED | COMBINATORIAL SUMS | APOSTOL-BERNOULLI | Eulerian polynomial | Faaa di Bruno's formula | Stirling number | Explicit expression
Journal Article
International Journal of Multiphase Flow, ISSN 0301-9322, 03/2020, Volume 124, Issue C, p. 103182
•Particle behavior in turbulent flows near a boundary is strongly affected by particle-particle collisions.•For particle-laden flows with a vast number of... 
Particle-laden flows | Wall-bounded turbulence | Computational particles | Four-way coupling | Eulerian-Lagrangian | LADEN TURBULENT FLOWS | TRANSPORT | MECHANICS | LARGE-EDDY SIMULATION | HOMOGENEOUS TURBULENCE | DRAG | VERTICAL CHANNEL | NUMERICAL-SIMULATION
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 2011, Volume 18, Issue 1, pp. 1 - 10
We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes... 
Eulerian-catalan number | Dyck permutation | Dyck path | Ballot sequence | MATHEMATICS | MATHEMATICS, APPLIED | Eulerian-Catalan number
Journal Article
Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 01/2010, Volume 17, Issue 1, pp. 121 - 126
In the present paper we propose a new proof of the Grosset-Veselov formula connecting one-soliton solution of the Korteweg-de Vries equation to the Bernoulli... 
Eulerian numbers | KdV equation | soliton | Bernoulli numbers | Riccati's equation | POLYNOMIALS | PHYSICS, MATHEMATICAL
Journal Article
Chemical Engineering Science, ISSN 0009-2509, 04/2019, Volume 198, pp. 334 - 351
[Display omitted] •DLM/FD-SIM numerical method for the simulation of convective mass transfer past reactive obstacles.•Numerical method validated on multiple... 
Sharp Interface Method | Sherwood number | Thiele modulus | Chemical reaction | Catalyst particle | Mass transfer | HEAT-TRANSFER | PACKED-BED | CATALYST | ENGINEERING, CHEMICAL | DIRECT NUMERICAL-SIMULATION | CHANNEL | CYLINDERS | EULERIAN APPROACH | PARTICULATE FLOWS | IMMERSED BOUNDARY METHOD | EQUATION | Engineering Sciences | Mathematics
Journal Article
Markov Processes and Related Fields, ISSN 1024-2953, 2015, Volume 21, Issue 3P, pp. 779 - 790
I describe the occurrence of Eulerian numbers and Stirling numbers of the second kind in the combinatorics of the "Statistical Curse of the Second Half Rank"... 
Eulerian numbers | Stirling numbers | Stochastic processes | Random permutations | random permutations | STATISTICS & PROBABILITY | stochastic processes
Journal Article
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