Plethystic翻译
In mathematics, the plethystic exponential is a certain operator defined on (formal) power series which, like the usual exponential function, translates addition into multiplication. This exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials in many variables. Its name comes from the operation called plethysm, defined in the context of … WebbA Polytheistic Conception of the Sciences and the Virtues of Deep Variety. Umbrella and Polytheistic Scientific Disciplines and Their Elites. The Deities Are Many: A Polytheistic …
Plethystic翻译
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Webbtic expressions. In particular, we show how plethystic transforms of quasisymmet-ric functions provide combinatorial interpretations for plethystic evaluations of skew Schur functions and Lascoux–Leclerc–Thibon (LLT) polynomials. Section 5 derives the plethystic Cauchy formulas and illustrates their use by giving an application (due WebbBy studying non-commutative series in an infinite alphabet, we introduce shift-plethystic trees and a class of integer compositions as new combinatorial models for the Rogers–Ramanujan identities. We prove that the language associated to shift-plethystic trees can be expressed as a non-commutative generalization of the Rogers–Ramanujan …
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