Results 61 to 70 of about 1,269,170 (176)

Success Run Waiting Times and Fuss-Catalan Numbers

Journal of Probability and Statistics, 2015
We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run of k consecutive successes in a sequence of independent Bernoulli trials, that is, the ...
S. J. Dilworth, S. R. Mane
doaj   +1 more source

On generalized bihyperbolic Mersenne numbers [PDF]

Mathematica Bohemica
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
doaj   +1 more source

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
doaj   +1 more source

Some explicit expressions for twisted q-analogues of Catalan numbers and polynomials [PDF]

Discrete Mathematics Letters, 2022
Dongkyu Lim
doaj   +1 more source

On ideal convergence of sequences via Catalan matrix operator

Miskolc Mathematical Notes
Catalan sequence initially introduced by Euler but named after Eugene Catalan has found abundant applications in the fields of probability theory, number theory, analysis, combinatorics etc.
Vakeel Ahmad Khan, Mikail Et, Umme Tuba
doaj   +1 more source

Ears of triangulations and Catalan numbers

Discrete Mathematics, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferran Hurtado, Marc Noy
openaire   +3 more sources

A New Combinatorial Identity for Catalan Numbers

, 2017
In this article, we prove a conjecture about the equality of two generating functions described in "From Parking Functions to Gelfand Pairs (Aker, Can 2012)" attached to two sets whose cardinalities are given by Catalan numbers: We establish a ...
Aker, Kursat, Gursoy, Aysin Erkan
core  

On dual and hyper-dual $k$-Leonardo numbers [PDF]

Mathematica Bohemica
We describe new classes of dual and hyper-dual numbers whose coefficients consist of the $k$-Leonardo numbers. We will call these numbers dual $k$-Leonardo numbers and hyper-dual $k$-Leonardo numbers, respectively.
Tülay Yağmur
doaj   +1 more source

Proofs of two conjectures involving sums of normalized Narayana numbers

Demonstratio Mathematica
Narayana numbers are well-known and have many applications in the field of combinatorics. The Narayana numbers form a triangular array, where the sum of the nth row is the nth Catalan number.
Goldman Ron, Simeonov Plamen, Zafiris Vasilis   +2 more
doaj   +1 more source

On a generalization of the Gadovan numbers [PDF]

Mathematica Moravica
In this paper, we define (k, l)-Gadovan numbers. We give the Binet-like formula, the generating functions, the exponential generating function of the (k, l)-Gadovan numbers. Also, we derive Cassinilike identity, Catalan-like identity, Vajda-like identity,
Özkan Engın, Eser Engın, Uysal Mıne
doaj   +1 more source