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

D. M. Jackson; M. Yip

doi:10.1007/s00026-006-0300-z

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

D. M. Jackson, M. Yip

Mathematics

Research output: Contribution to journal › Article › peer-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 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(k₁, . . . , k_r). We also consider the limit lim_n,r→∞(-1)ⁿS_k1,..., k _r(1-r)/rⁿ subject to the condition that lim _n,r→∞ P_q(k₁, . . . , k _r)/r exists for q = 1, 2, . . ..

Original language	English
Pages (from-to)	463-480
Number of pages	18
Journal	Annals of Combinatorics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/s00026-006-0300-z
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

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10.1007/s00026-006-0300-z

Cite this

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title = "A symmetric function resolution of the number of permutations with respect to block-stable elements",

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, . . ..",

keywords = "Bosonic model, Enumerative problem, Quantum computing, Symmetric functions",

author = "Jackson, {D. M.} and M. Yip",

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.",

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N2 - 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, . . ..

AB - 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, . . ..

KW - Bosonic model

KW - Enumerative problem

KW - Quantum computing

KW - Symmetric functions

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JF - Annals of Combinatorics

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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