## Abstract

We consider a question raised by Suhov and Voice from quantum information theory and quantum computing. An element of a partition of {1, . . . ,n} is said to be block-stable for π ∈ G-fractur sign_{n} if it is not moved to another block under the action of π. The problem concerns the determination of the generating series S_{k1},...,k_{r} (u) for elements of G-fractur sign_{n} with respect to the number of blockstable elements of a canonical partition of a finite n-set, with block sizes k _{1};, . . . , k_{r}, in terms of the moment (power) sums p _{q}(k_{1}, . . . , k_{r}). We also consider the limit lim_{n,r→∞}(-1)^{n}S_{k1},..., k _{r}(1-r)/r^{n} subject to the condition that lim _{n,r→∞} P_{q}(k_{1}, . . . , k _{r})/r exists for q = 1, 2, . . ..

Original language | English |
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Pages (from-to) | 463-480 |

Number of pages | 18 |

Journal | Annals of Combinatorics |

Volume | 10 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2006 |

### Bibliographical note

Funding Information:Acknowledgments. The authors thank Y. Suhov for introducing them to this question and its background. This work was supported by a NSERC Discovery Grant to DMJ, and a NSERC undergraduate research award to MY.

## Keywords

- Bosonic model
- Enumerative problem
- Quantum computing
- Symmetric functions

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics