An Approach to the Herzog-Schönheim Conjecture Using Automata

Fabienne Chouraqui

doi:10.1007/978-3-030-48516-0_5

An Approach to the Herzog-Schönheim Conjecture Using Automata

Fabienne Chouraqui

Department of Mathematics, Physics and Computer Science (Oranim Campus)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Let G be a group and H₁,.., H_s be subgroups of G of indices d₁,...,d_s respectively. In 1974, M. Herzog and J. Schönheim conjectured that if {H_iα_i}_i=1^i=s, (Formula Presented), is a coset partition of G, then d₁,...,d_s cannot be distinct. In this paper, we present a new approach to the Herzog-Schönheim conjecture based on automata and present a translation of the conjecture as a problem on automata.

Original language	English
Title of host publication	Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings
Editors	Nataša Jonoska, Dmytro Savchuk
Publisher	Springer
Pages	55-68
Number of pages	14
ISBN (Print)	9783030485153
DOIs	https://doi.org/10.1007/978-3-030-48516-0_5
State	Published - 2020
Event	24th International Conference on Developments in Language Theory, DLT 2020 - Tampa, United States Duration: 11 May 2020 → 15 May 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12086 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	24th International Conference on Developments in Language Theory, DLT 2020
Country/Territory	United States
City	Tampa
Period	11/05/20 → 15/05/20

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2020.

Keywords

Automata
Coset partitions
Free groups
The Herzog-Schönheim conjecture

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-48516-0_5

Cite this

Chouraqui, F. (2020). An Approach to the Herzog-Schönheim Conjecture Using Automata. In N. Jonoska, & D. Savchuk (Eds.), Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings (pp. 55-68). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12086 LNCS). Springer. https://doi.org/10.1007/978-3-030-48516-0_5

Chouraqui, Fabienne. / An Approach to the Herzog-Schönheim Conjecture Using Automata. Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings. editor / Nataša Jonoska ; Dmytro Savchuk. Springer, 2020. pp. 55-68 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Let G be a group and H1,.., Hs be subgroups of G of indices d1,...,ds respectively. In 1974, M. Herzog and J. Sch{\"o}nheim conjectured that if {Hiαi}i=1i=s, (Formula Presented), is a coset partition of G, then d1,...,ds cannot be distinct. In this paper, we present a new approach to the Herzog-Sch{\"o}nheim conjecture based on automata and present a translation of the conjecture as a problem on automata.",

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Chouraqui, F 2020, An Approach to the Herzog-Schönheim Conjecture Using Automata. in N Jonoska & D Savchuk (eds), Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12086 LNCS, Springer, pp. 55-68, 24th International Conference on Developments in Language Theory, DLT 2020, Tampa, United States, 11/05/20. https://doi.org/10.1007/978-3-030-48516-0_5

An Approach to the Herzog-Schönheim Conjecture Using Automata. / Chouraqui, Fabienne.
Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings. ed. / Nataša Jonoska; Dmytro Savchuk. Springer, 2020. p. 55-68 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12086 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Chouraqui F. An Approach to the Herzog-Schönheim Conjecture Using Automata. In Jonoska N, Savchuk D, editors, Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings. Springer. 2020. p. 55-68. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-48516-0_5

An Approach to the Herzog-Schönheim Conjecture Using Automata

Abstract

Publication series

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Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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