A symmetric function resolution of the number of permutations with respect to block-stable elements

D. M. Jackson, M. Yip

Research output: Contribution to journalArticlepeer-review

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 signn if it is not moved to another block under the action of π. The problem concerns the determination of the generating series Sk1,...,kr (u) for elements of G-fractur signn with respect to the number of blockstable elements of a canonical partition of a finite n-set, with block sizes k 1;, . . . , kr, in terms of the moment (power) sums p q(k1, . . . , kr). We also consider the limit limn,r→∞(-1)nSk1,..., k r(1-r)/rn subject to the condition that lim n,r→∞ Pq(k1, . . . , k r)/r exists for q = 1, 2, . . ..

Original languageEnglish
Pages (from-to)463-480
Number of pages18
JournalAnnals of Combinatorics
Volume10
Issue number4
DOIs
StatePublished - 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

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