Results 51 to 60 of about 302 (115)
The Generating Function of the Catalan Numbers and Lower Triangular Integer Matrices
, 2017 In the paper, by the Faà di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating ...
Feng Qi (祁锋) +2 more
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A new approach to the r-Whitney numbers by using combinatorial differential calculus
Acta Universitatis Sapientiae: Mathematica, 2019 In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar G := {y → yxm, x → x}.
Méndez Miguel A., Ramírez José L.
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A note involving two-by-two matrices of the k-Pell and k-Pell-Lucas sequences
, 2013 We use a diagonal matrix for getting the Binet’s formula for k-Pell sequence Also the n power of the generating matrix for k-Pell-Lucas sequence is established and basic properties involving the determinant allow us to obtain its Cassini’s identity ...
P. Catarino
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The log-concavity of the q-derangement numbers of type B
Open Mathematics, 2018 Recently, Chen and Xia proved that for n ≥ 6, the q-derangement numbers Dn(q) are log-concave except for the last term when n is even. In this paper, employing a recurrence relation for DnB(q) $\begin{array}{} \displaystyle D^B_n(q) \end{array ...
Liu Eric H., Du Wenjing
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Proofs of Conjectures about Pattern-Avoiding Linear Extensions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 After fixing a canonical ordering (or labeling) of the elements of a finite poset, one can associate each linear extension of the poset with a permutation.
Colin Defant
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The permutation class Av(4213,2143) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 We determine the structure of permutations avoiding the patterns 4213 and 2143. Each such permutation consists of the skew sum of a sequence of plane trees, together with an increasing sequence of points above and an increasing sequence of points to its ...
David Bevan
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A unimodality result in the enumeration of subgroups of a finite abelian group
, 1987 The number of subgroups of order pk in an abelian group G of order pn is a polynomial in p, o, (k; p), determined by the type A of G. It is well known that oa,(k; p) = a(n k; p).
L. M. Butler
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Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Super-strong Wilf equivalence classes of the symmetric group ${\mathcal S}_n$ on $n$ letters, with respect to the generalized factor order, were shown by Hadjiloucas, Michos and Savvidou (2018) to be in bijection with pyramidal sequences of consecutive ...
Ioannis Michos, Christina Savvidou
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Growing and Destroying Catalan-Stanley Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers.
Benjamin Hackl, Helmut Prodinger
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Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials
, 2014 In this paper, we consider Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.MSC:05A15, 05A40 ...
Dae San Kim +3 more
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