Results 41 to 50 of about 62,131 (208)
Polynomial Triangles Revisited [PDF]
, 2012 A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to fill this gap.
Mohammedia Morocco, Nour-eddine Fahssi
core
Weighted Lattice Paths Enumeration by Gaussian Polynomials
, 2017 The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a combinatorial ...
Martinjak, Ivica, Zubac, Ivana
core +1 more source
Binomial Fibonacci sums from Chebyshev polynomials
, 2023 25 ...
Adegoke, Kunle +2 more
openaire +3 more sources
Advanced Science, EarlyView.Zhang et al. identify M7core, a critical cGAS‐STING pathway‐driven gene signature that is activated in most lupus patients’ blood and links to lupus disease severity, lymphopenia, and lupus nephritis. They further reveal the diagnostic and pathogenic characteristics of M7core and emphasize the importance of assessing pathway activity before initiating ...
Lele Zhang +13 more
wiley +1 more source
$q$-DEFORMED RATIONALS AND $q$-CONTINUED FRACTIONS
Forum of Mathematics, Sigma, 2020 We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$-deformed Pascal
SOPHIE MORIER-GENOUD, VALENTIN OVSIENKO
doaj +1 more source
Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
doaj +1 more source
Polynomial Functors of Modules [PDF]
, 2014 We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise criterion for a ...
Harry Martinson Aniara +1 more
core
Umbral calculus, binomial enumeration and chromatic polynomials [PDF]
Transactions of the American Mathematical Society, 1988 We develop the concept of partition categories, in order to extend the Mullin-Rota theory of binomial enumeration, and simultaneously to provide a natural setting for recent applications of the Roman-Rota umbral calculus to computations in algebraic topology. As a further application, we describe a generalisation of the chromatic polynomial of a graph.
openaire +2 more sources
Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley +1 more source
Polynomial solutions of binomial congruences [PDF]
Journal of the Australian Mathematical Society, 1960 Polynomial solutions of a few binomial congruences have been known for a long time. For instance Legendre showed that the congruence has a solution this being the expansion of as far as the term of degree m — 3. [1] It seems that only restricted types, e.g. (1), have been investigated.
openaire +1 more source