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Algebras and Representation Theory, ISSN 1386-923X, 6/2018, Volume 21, Issue 3, pp. 511 - 527
Starting from the invariant theory of binary forms, we extend the classical notion of covariants and introduce the ring of T $\mathcal {T}$-covariants. This... 
13A50 | 11P81 | 16W50 | Associative Rings and Algebras | 05A40 | Non-associative Rings and Algebras | Orthogonal polynomials | Commutative Rings and Algebras | Mathematics | Translation invariance | Cumulants
Journal Article
Algebras and Representation Theory, ISSN 1386-923X, 06/2018, Volume 21, Issue 3, pp. 511 - 527
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s10468-017-9724-x Starting... 
Translation invariance | Cumulants | Orthogonal polynomials
Journal Article
Advances in Mathematics, ISSN 0001-8708, 11/2016, Volume 303, pp. 123 - 150
We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line... 
Symmetric polynomials | Binary forms | Apolarity | Orthogonal polynomials | MATHEMATICS
Journal Article
The Annals of Statistics, ISSN 0090-5364, 4/2013, Volume 41, Issue 2, pp. 982 - 1004
Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated... 
Integers | Algebra | Generating function | Random sampling | Spectral theory | Eigenvalues | Umbra | Scalars | Polynomials | Mathematical functions | Random matrix | Free cumulant | Polykays | Cumulant of traces | cumulant of traces | polykays | SYMMETRIC GROUP | CUMULANTS | STATISTICS & PROBABILITY | free cumulant | 60B20 | 62F12 | 46L53
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 2/2011, Volume 33, Issue 1, pp. 141 - 151
We prove two formulae expressing the Kerov polynomial Σ k as a weighted sum over the set of noncrossing partitions of the set {1,…,k+1}. We also give a... 
Normalized characters | Convex and Discrete Geometry | Symmetric group | Symmetric functions | Noncrossing partitions | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Kerov polynomials | Computer Science, general | Combinatorics | MATHEMATICS | SYMMETRIC-GROUPS | POSITIVITY
Journal Article
Journal of Statistical Planning and Inference, ISSN 0378-3758, 2012, Volume 142, Issue 2, pp. 423 - 429
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of... 
Linear recurrences | Sheffer sequences | Classical umbral calculus | Dyck paths | UMBRAL CALCULUS | SEQUENCES | PATHS | STATISTICS & PROBABILITY | SHEFFER POLYNOMIALS
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 11/2016, Volume 58, pp. 225 - 237
Via the chip-firing game, a class of Schur positive symmetric functions depending on four parameters is introduced for any labeled connected simple graph.... 
MATHEMATICS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 03/2011, Volume 217, Issue 13, pp. 6286 - 6295
A new algorithm for computing the multivariate Faà di Bruno's formula is provided. We use a symbolic approach based on the classical umbral calculus that turns... 
Faà di Bruno's formula | Multivariate Hermite polynomial | Multivariate cumulant | Multivariate composite function | Classical umbral calculus | POLYNOMIALS | MATHEMATICS, APPLIED | DIBRUNO,FAA | Faa di Bruno's formula | CUMULANTS | Mathematical models | Calculus | Algorithms | Computation | Mathematical analysis
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 2010, Volume 31, Issue 7, pp. 1792 - 1804
We provide a unifying polynomial expression giving moments in terms of cumulants, and vice versa, holding in the classical, boolean and free setting. This is... 
MATHEMATICS | CLASSICAL UMBRAL CALCULUS | NON-CROSSING PARTITIONS | MULTIPLICATIVE FUNCTIONS | LATTICE | Fourier transforms | Construction | Convolution | Vices | Byproducts | Boolean algebra | Joints | Combinatorial analysis
Journal Article
Annali di Matematica Pura ed Applicata, ISSN 0373-3114, 9/2011, Volume 190, Issue 3, pp. 489 - 506
We revisit the theory of Sheffer sequences by means of the formalism introduced in Rota and Taylor (SIAM J Math Anal 25(2):694–711, 1994) and developed in Di... 
Lagrange inversion formula | Umbral calculus | Connection constants | 11B83 | 05A40 | Mathematics, general | Mathematics | Sheffer sequences | Riordan arrays | 05A15 | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENCES | WAVELETS | Computer science
Journal Article
Bernoulli, ISSN 1350-7265, 5/2008, Volume 14, Issue 2, pp. 440 - 468
Through the classical umbral calculus, we provide a unifying syntax for single and multivariate k-statistics, polykays and multivariate polykays. From a... 
Integers | Equivalence relation | Umbral calculus | Multisets | Factorials | Mathematical lattices | Umbra | Polynomials | Mathematics | Random variables | Symmetric polynomials | Polykays | k-statistics | Cumulants | cumulants | polykays | symmetric polynomials | umbral calculus | STATISTICS & PROBABILITY | CLASSICAL UMBRAL CALCULUS | FORMULA | WAVELETS | PARTITION LATTICES | MOMENTS
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 2006, Volume 27, Issue 3, pp. 394 - 413
We provide an algebraic setting for cumulants and factorial moments via the classical umbral calculus. Our main tools are the compositional inverse of the... 
MATHEMATICS | COMBINATORICS
Journal Article
Computational Statistics and Data Analysis, ISSN 0167-9473, 2008, Volume 52, Issue 11, pp. 4909 - 4922
By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A... 
CUMULANTS | STATISTICS & PROBABILITY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 2006, Volume 19, Issue 9, pp. 968 - 975
Through the classical umbral calculus, we provide new, compact and easy to handle expressions for k -statistics, and more generally for U -statistics. In... 
Umbral calculus | Symmetric polynomials | [formula omitted]-Statistics | Joint cumulants | U-Statistics | k-Statistics | MATHEMATICS, APPLIED | joint cumulants | symmetric polynomials | k-statistics | umbral calculus
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 2/2006, Volume 12, Issue 1, pp. 27 - 36
We explore compactly supported scaling functions of wavelet theory by means of classical umbral calculus as reformulated by Rota and Taylor. We set a theory of... 
Abstract Harmonic Analysis | Fourier Analysis | Signal, Image and Speech Processing | Approximations and Expansions | Mathematics | Applications of Mathematics | Partial Differential Equations | Wavelet | Scaling equation | Umbral calculus | wavelet | MATHEMATICS, APPLIED | BASES | scaling equation | FILTERS
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2001, Volume 41, Issue 9, pp. 1109 - 1124
Through the notion of enriched species, we develop a bijective calculus set-theoretic counterpart of the theory of binomial enumeration. 
Enriched species | Umbral calculus | Möbius species | Polynomials of binomial type | MATHEMATICS, APPLIED | Mobius species | enriched species | COMBINATORIAL THEORY | umbral calculus | polynomials of binomial type
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 04/2006, Volume 16, Issue 2, pp. 377 - 396
We construct the analog of the plactic monoid for the super semistandard Young tableaux over a signed alphabet. This is done by developing a generalization of... 
Plactic monoid | Young tableau | RSK-correspondence | MATHEMATICS | HOOK YOUNG-DIAGRAMS | plactic monoid | COMBINATORICS | Algorithms
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 13, pp. 6286 - 6295
A new algorithm for computing the multivariate Faà di Bruno’s formula is provided. We use a symbolic approach based on the classical umbral calculus that turns... 
Multivariate Hermite polynomial | Multivariate cumulant | Faà di Bruno’s formula | Multivariate composite function | Classical umbral calculus
Journal Article
08/2009
We prove a formula expressing the Kerov polynomial $\Sigma_k$ as a weighted sum over the lattice of noncrossing partitions of the set $\{1,...,k+1\}$. In... 
Journal Article
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