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Weighted Catalan convolution and $(q,2)$-Fock space

Yungang Lu

Abstract

Motivated by the study of certain combinatorial properties of $(q,2)$-Fock space, we compute explicitly a sequence driven by the Catalan's convolution and parameterized by $1+q$. As an application of this explicit form, we calculate the number of pair partitions involved in the determination of the vacuum--moments of the field operator defined on the $(q,2)$-Fock space.

Weighted Catalan convolution and $(q,2)$-Fock space

Abstract

Motivated by the study of certain combinatorial properties of -Fock space, we compute explicitly a sequence driven by the Catalan's convolution and parameterized by . As an application of this explicit form, we calculate the number of pair partitions involved in the determination of the vacuum--moments of the field operator defined on the -Fock space.
Paper Structure (6 sections, 4 theorems, 81 equations)

This paper contains 6 sections, 4 theorems, 81 equations.

Table of Contents

  1. Introduction
  2. Pair partitions and some related concepts; Elementary properties of $(q,2)-$Fock space
  3. Pair partitions and some related concepts
  4. $(q,2)-$Fock space
  5. Weighted Catalan's convolution
  6. An application

Key Result

Proposition 3.1

On the $(q,2)-$Fock space over $\mathcal{H}$, or equivalently,

Theorems & Definitions (16)

  • Remark 2.1
  • Remark 2.2
  • Definition 2.3
  • Remark 2.4
  • Remark 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition 2.8
  • Proposition 3.1
  • proof
  • ...and 6 more