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

Producción científica: Article › revisión exhaustiva

Resumen

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, . . ..

Idioma original	English
Páginas (desde-hasta)	463-480
Número de páginas	18
Publicación	Annals of Combinatorics
Volumen	10
N.º	4
DOI	https://doi.org/10.1007/s00026-006-0300-z
Estado	Published - dic 2006

Nota bibliográfica

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.

Financiación

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.

Financiadores
Natural Sciences and Engineering Research Council of Canada

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1007/s00026-006-0300-z

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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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AU - Yip, M.

N1 - 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.

PY - 2006/12

Y1 - 2006/12

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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UR - https://www.scopus.com/pages/publications/33846949395#tab=citedBy

U2 - 10.1007/s00026-006-0300-z

DO - 10.1007/s00026-006-0300-z

M3 - Article

AN - SCOPUS:33846949395

SN - 0218-0006

VL - 10

SP - 463

EP - 480

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 4

ER -

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

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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