On the isomorphism problem for cyclic combinatorial objects

Mikhail Muzychuk

doi:10.1016/s0012-365x(98)00264-7

On the isomorphism problem for cyclic combinatorial objects

Mikhail Muzychuk

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

We prove that the number of cyclic combinatorial objects on n elements isomorphic to a given one is less than or equal to φ(n). We also show that if any two prime divisors p ≠ q of n satisfy the property p/(q - 1),q/(p - 1), then the isomorphism problem for cyclic combinatorial objects on n elements may be reduced to the one on prime power number of elements.

Original language	English
Pages (from-to)	589-606
Number of pages	18
Journal	Discrete Mathematics
Volume	197-198
DOIs	https://doi.org/10.1016/s0012-365x(98)00264-7
State	Published - 28 Feb 1999
Externally published	Yes

Keywords

Combinatorial object
Cyclic group
Isomorphism problem

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/s0012-365x(98)00264-7

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title = "On the isomorphism problem for cyclic combinatorial objects",

abstract = "We prove that the number of cyclic combinatorial objects on n elements isomorphic to a given one is less than or equal to φ(n). We also show that if any two prime divisors p ≠ q of n satisfy the property p/(q - 1),q/(p - 1), then the isomorphism problem for cyclic combinatorial objects on n elements may be reduced to the one on prime power number of elements.",

keywords = "Combinatorial object, Cyclic group, Isomorphism problem",

author = "Mikhail Muzychuk",

note = "Funding Information: E-mail: [email protected]. I This research was supported by the Grant No. 1-0333-263.06/93 from the German-Israeli Foundation for Scientific Research and Development.",

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Y1 - 1999/2/28

N2 - We prove that the number of cyclic combinatorial objects on n elements isomorphic to a given one is less than or equal to φ(n). We also show that if any two prime divisors p ≠ q of n satisfy the property p/(q - 1),q/(p - 1), then the isomorphism problem for cyclic combinatorial objects on n elements may be reduced to the one on prime power number of elements.

AB - We prove that the number of cyclic combinatorial objects on n elements isomorphic to a given one is less than or equal to φ(n). We also show that if any two prime divisors p ≠ q of n satisfy the property p/(q - 1),q/(p - 1), then the isomorphism problem for cyclic combinatorial objects on n elements may be reduced to the one on prime power number of elements.

KW - Combinatorial object

KW - Cyclic group

KW - Isomorphism problem

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DO - 10.1016/s0012-365x(98)00264-7

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VL - 197-198

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JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

On the isomorphism problem for cyclic combinatorial objects

Abstract

Keywords

ASJC Scopus subject areas

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