#generating functions
13 papers match
The Sixth Moment of Random Determinants for Arbitrarily Distributed Random Entries
Dominik Beck, Zelin Lv, Aaron Potechin
The paper derives a closed‑form expression for the sixth moment of the determinant of an n×n matrix with i.i.d. entries of any distribution, using a combinatorial decomposition of…
An Invertible Family of Hurwitz--Lerch Type Functions Associated with -Augmented Centered Triangular Numbers
Noel B. Lacpao, Rushel S. Acope, Marlon S. Frias +3
The paper introduces a family of Hurwitz–Lerch type functions whose coefficients are k‑augmented centered triangular numbers, and derives convergence conditions, reduction and inve…
On the Irreducibility of the Differential Operators Associated to Random Walks in the Standard Euclidean Lattice
Dorin DumitraÅcu, Liviu Suciu
The paper analyzes generating functions for combinatorial sequences arising from random walks on the standard Euclidean lattice, proving that the associated differential operators…
The height of skew Dyck paths with two variants of downsteps
Helmut Prodinger
The paper analyzes skew Dyck paths that include two different down‑step types, using generating functions, the kernel method, and linear systems to enumerate these paths and determ…
Alternating adjacent-sum polytopes: transfer matrices and Ehrhart series
Xinru Jiang, Suzhen Wen, Yueming Zhong
The paper investigates a family of alternating adjacent‑sum lattice polytopes, deriving explicit transfer‑matrix representations and detailed Ehrhart generating functions, recurren…
On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions
Johann Stumpenhusen
The paper introduces a new variant of log‑concavity for families of polynomials and proves that specific D'Arcais polynomials satisfy this property at particular points.
Expansions of in Shifted Binomial Bases and a Modular Symmetry Criterion
Abdelhai Doukali
The paper derives a closed‑form expression for the coefficients when expanding the polynomial \(\binom{pn}{p+r}\) in a shifted binomial basis, identifies a modular condition (r ≡ 1…
Study on Morgan-Voyce type polynomials with Euler-Seidel algorithm
Taekyun Kim, Dae san Kim
The paper defines new families of Morgan‑Voyce type polynomials, derives their explicit formulas, recurrence relations and exponential generating functions, and links them to Euler…
On Factorizing Aggregate Counting Distributions into Independent Latent Processes
Israel Klich
The paper develops a mathematical framework for decomposing the distribution of an aggregate counting variable into independent latent counting processes by studying positive facto…
Power-law and log-periodic degree tails for a family of probability generating function equations arising in evolving networks
Qunqiang Feng, Xiao-Ming Fu, Tianyang Sun
The paper analyzes a probability generating function equation that describes the limiting degree distribution of certain evolving network models, proving a unique solution with a p…
On generating functions and Mehler--Heine formulas for discrete Charlier and Meixner Sobolev-type orthogonal polynomials
Anier Soria Lorente, Junior Michel
The paper constructs a unified generating‑function framework for Sobolev‑type discrete Charlier and Meixner orthogonal polynomials and uses it to derive Mehler‑Heine asymptotic for…
-Convex Polyominoes by Semi-perimeter
Andrew R. Conway, Anthony J. Guttmann
The paper proposes a conjectured generating function for counting k‑convex polyominoes based on their semi‑perimeter.
Arithmetic Properties for -Color Analogue of Simultaneously -Regular and -Distinct Partitions
Anjelin Mariya Johnson, S. N. Fathima
The paper studies generating functions for three‑color partitions that are simultaneously s‑regular and t‑distinct, and proves infinite families of congruences modulo powers of 3 f…
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