42 citations · 75 across the 9 of their papers we have counts for
6 papers · 1 filter
A new explicit formula for Kerov polynomials
P. Petrullo, D. Senato
We prove a formula expressing the Kerov polynomial as a weighted sum over the lattice of noncrossing partitions of the set . In particular, such a formula is r…
Super RSK-algorithms and super plactic monoid
R. La Scala, V. Nardozza, D. Senato
We construct the analogue of the plactic monoid for the super semistandard Young tableaux over a signed alphabet. This is done by developing a generalization of the Knuth's relatio…
The classical umbral calculus: Sheffer sequences
E. Di Nardo, H. Niederhausen, D. Senato
Following the approach of Rota and Taylor \cite{SIAM}, we present an innovative theory of Sheffer sequences in which the main properties are encoded by using umbrae. This syntax al…
An instance of umbral methods in representation theory: the parking function module
P. Petrullo, D. Senato
We test the umbral methods introduced by Rota and Taylor within the theory of representation of symmetric group. We define a simple bijection between the set of all parking functio…
A unifying framework for -statistics, polykays and their multivariate generalizations
Elvira Di Nardo, Giuseppe Guarino, Domenico Senato
Through the classical umbral calculus, we provide a unifying syntax for single and multivariate -statistics, polykays and multivariate polykays. From a combinatorial point of vi…
A symbolic method for k-statistics
E. Di Nardo, D. Senato
Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U-statistics. In addition such a symbolic metho…