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Stokes, Klara
Publications (7 of 7) Show all publications
Lundqvist, S., Stokes, K. & Öhman, L.-D. (2023). Applying the pebble game algorithm to rod configurations. In: EuroCG 2023: Book of abstracts. Paper presented at The 39th European workshop on computational geometry (EuroCG 2023), Barcelona, Spain, March 29-31, 2023. , Article ID 41.
Open this publication in new window or tab >>Applying the pebble game algorithm to rod configurations
2023 (English)In: EuroCG 2023: Book of abstracts, 2023, article id 41Conference paper, Published paper (Refereed)
Abstract [en]

We present results on rigidity of structures of rigid rods connected in joints: rod configurations. The underlying combinatorial structure of a rod configuration is an incidence structure. Our aim is to find simple ways of determining which rod configurations admit non-trivial motions, using the underlying incidence structure.

Rigidity of graphs in the plane is well understood. Indeed, there is a polynomial time algorithm for deciding whether most realisations of a graph are rigid. One of the results presented here equates rigidity of sufficiently generic rod configurations to rigidity of a related graph. As a consequence, itis possible to determine the rigidity of rod configurations using the previously mentioned polynomial time algorithm. We use this to show that all v3-configurations on up to 15 points and all triangle-free v3-configurations on up to 20 points are rigid in regular position, if such a realisation exists. We also conjecture that the smallest v3-configuration that is flexible in regular position is a previously known 283-configuration. 

National Category
Discrete Mathematics Geometry
Identifiers
urn:nbn:se:umu:diva-215548 (URN)
Conference
The 39th European workshop on computational geometry (EuroCG 2023), Barcelona, Spain, March 29-31, 2023
Available from: 2023-10-22 Created: 2023-10-22 Last updated: 2023-10-23Bibliographically approved
Lundqvist, S., Stokes, K. & Öhman, L.-D. (2023). Exploring the rigidity of planar configurations of points and rods. Discrete Applied Mathematics, 336, 68-82
Open this publication in new window or tab >>Exploring the rigidity of planar configurations of points and rods
2023 (English)In: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 336, p. 68-82Article in journal (Refereed) Published
Abstract [en]

In this article we explore the rigidity of realizations of incidence geometries consisting of points and rigid rods: rod configurations. We survey previous results on the rigidity of structures that are related to rod configurations, discuss how to find realizations of incidence geometries as rod configurations, and how this relates to the 2-plane matroid. We also derive further sufficient conditions for the minimal rigidity of k-uniform rod configurations and give an example of an infinite family of minimally rigid 3-uniform rod configurations failing the same conditions. Finally, we construct v3-configurations that are flexible in the plane, and show that there are flexible v3-configurations for all sufficiently large values of v.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Combinatorial rigidity, Incidence geometry, Rod configuration
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-208092 (URN)10.1016/j.dam.2023.03.030 (DOI)000983170400001 ()2-s2.0-85153509834 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation, 2020.0001Knut and Alice Wallenberg Foundation, 2020.0007
Available from: 2023-05-09 Created: 2023-05-09 Last updated: 2023-09-05Bibliographically approved
Stokes, K. (2023). Geometric decoding of subspace codes with explicit Schubert calculus applied to spread codes. Advances in mathematics of communications
Open this publication in new window or tab >>Geometric decoding of subspace codes with explicit Schubert calculus applied to spread codes
2023 (English)In: Advances in mathematics of communicationsArticle in journal (Refereed) Accepted
National Category
Geometry Discrete Mathematics Communication Systems
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-215549 (URN)
Available from: 2023-10-22 Created: 2023-10-22 Last updated: 2023-10-22
Leemans, D. & Stokes, K. (2023). Incidence geometries with trialities coming from maps with Wilson trialities. Innovations in Incidence Geometry, 20(2-3), 325-340
Open this publication in new window or tab >>Incidence geometries with trialities coming from maps with Wilson trialities
2023 (English)In: Innovations in Incidence Geometry, ISSN 2640-7337, Vol. 20, no 2-3, p. 325-340Article in journal (Refereed) Published
Abstract [en]

Triality is a classical notion in geometry that arose in the context of the Lie groups of type D4. Another notion of triality, Wilson triality, appears in the context of reflexible maps. We build a bridge between these two notions, showing how to construct an incidence geometry with a triality from a map that admits a Wilson triality. We also extend a result by Jones and Poulton, showing that for every prime power q, the group L2 (q3) has maps that admit Wilson trialities but no dualities.

Place, publisher, year, edition, pages
Mathematical Sciences Publishers, 2023
Keywords
incidence geometry, maps, projective special linear groups, triality
National Category
Geometry
Identifiers
urn:nbn:se:umu:diva-214970 (URN)10.2140/iig.2023.20.325 (DOI)2-s2.0-85172363093 (Scopus ID)
Available from: 2023-10-16 Created: 2023-10-16 Last updated: 2023-10-23Bibliographically approved
Lundqvist, S., Stokes, K. & Öhman, L.-D. (2023). When is a planar rod configuration infinitesimally rigid?. Discrete & Computational Geometry
Open this publication in new window or tab >>When is a planar rod configuration infinitesimally rigid?
2023 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444Article in journal (Refereed) Epub ahead of print
Abstract [en]

We investigate the rigidity properties of rod configurations. Rod configurations are realizations of rank two incidence geometries as points (joints) and straight lines (rods) in the Euclidean plane, such that the lines move as rigid bodies, connected at the points. Note that not all incidence geometries have such realizations. We show that under the assumptions that the rod configuration exists and is sufficiently generic, its infinitesimal rigidity is equivalent to the infinitesimal rigidity of generic frameworks of the graph defined by replacing each rod by a cone over its point set. To put this into context, the molecular conjecture states that the infinitesimal rigidity of rod configurations realizing 2-regular hypergraphs is determined by the rigidity of generic body and hinge frameworks realizing the same hypergraph. This conjecture was proven by Jackson and Jordán in the plane, and by Katoh and Tanigawa in arbitrary dimension. Whiteley proved a version of the molecular conjecture for hypergraphs of arbitrary degree that have realizations as independent body and joint frameworks. Our result extends his result to hypergraphs that do not necessarily have realizations as independent body and joint frameworks, under the assumptions listed above.

Place, publisher, year, edition, pages
Springer Nature, 2023
Keywords
Combinatorial rigidity, Hypergraphs, Incidence geometries, Parallel redrawings, Rod configurations
National Category
Discrete Mathematics
Identifiers
urn:nbn:se:umu:diva-218895 (URN)10.1007/s00454-023-00617-7 (DOI)2-s2.0-85180169240 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation, 2020.0001Knut and Alice Wallenberg Foundation, 2020.0007
Available from: 2024-01-04 Created: 2024-01-04 Last updated: 2024-01-04
Forbes, A. D., Griggs, T. S. & Stokes, K. (2022). Existence results for pentagonal geometries. The Australasian Journal of Combinatorics, 82(1), 95-114
Open this publication in new window or tab >>Existence results for pentagonal geometries
2022 (English)In: The Australasian Journal of Combinatorics, ISSN 1034-4942, Vol. 82, no 1, p. 95-114Article in journal (Refereed) Published
Abstract [en]

New results on pentagonal geometries PENT(k, r) with block sizes k = 3 or k = 4 are given. In particular we completely determine the existence spectra for PENT(3, r) systems with the maximum number of opposite line pairs as well as those without any opposite line pairs. A wide-ranging result about PENT(3, r) with any number of opposite line pairs is proved. We also determine the existence spectrum of PENT(4, r) systems with eleven possible exceptions.

Place, publisher, year, edition, pages
University of Queensland Press, 2022
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-190889 (URN)2-s2.0-85121582191 (Scopus ID)
Available from: 2021-12-30 Created: 2021-12-30 Last updated: 2022-01-03Bibliographically approved
Mc Glue, C. & Stokes, K. (2022). Generating All Rigidity Circuits on at Most 10 Vertices and All Assur Graphs on at Most 11 Vertices. Journal of Integer Sequences, 25(1), Article ID 22.1.3.
Open this publication in new window or tab >>Generating All Rigidity Circuits on at Most 10 Vertices and All Assur Graphs on at Most 11 Vertices
2022 (English)In: Journal of Integer Sequences, E-ISSN 1530-7638, Vol. 25, no 1, article id 22.1.3Article in journal (Refereed) Published
Abstract [en]

We present an inventory and the enumeration of all non-isomorphic rigidity circuits on up to 10 vertices, as well as all non-isomorphic Assur graphs on up to 11 vertices. Assur graphs and Baranov trusses are closely related. We clarify the relation between Baranov trusses and (2, 3)-tight graphs on the one hand, and between Assur groups and Assur graphs on the other hand.

Place, publisher, year, edition, pages
University of Waterloo, 2022
Keywords
Assur graph, Rigidity circuit
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-191124 (URN)2-s2.0-85122162316 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation, 2020.0001Knut and Alice Wallenberg Foundation, 2020.0007
Available from: 2022-01-10 Created: 2022-01-10 Last updated: 2024-02-08Bibliographically approved
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