Page 268 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 268
COMBINATORIAL DESIGNS (MS-16)
References
[1] D. Crnkovic´, D. Dumicˇic´ Danilovic´, S. Rukavina, Enumeration of symmetric (45,12,3)
designs with nontrivial automorphisms, J. Algebra Comb. Discrete Struct. Appl. 3 (2016),
145–154.
[2] D. Crnkovic´, S. Rukavina, L. Simcˇic´, On triplanes of order twelve admitting an automor-
phism of order six and their binary and ternary codes, Util. Math. 103 (2017), 23–40.
Merging Combinatorial Design and Optimization: the Oberwolfach
Problem
Fabio Salassa, fabio.salassa@polito.it
Politecnico di Torino, Italy
Coauthors: Gabriele Dragotto, Tommaso Traetta, Marco Buratti, Federico Della Croce
Combinatorial optimization is a subset of mathematical optimization that is related to opera-
tions research, algorithm theory, and computational complexity theory. It consists of finding an
(optimal) object from a finite set of objects and in many such problems, exhaustive search is not
tractable. Combinatorial design theory is the part of combinatorial mathematics that deals with
the existence, construction and properties of systems of finite sets whose arrangements satisfy
generalized concepts of balance and/or symmetry. Combinatorial Design and Combinatorial
Optimization, though apparently different research fields, share common problems, such as for
example sudokus, covering arrays, tournament design and more in general problems that can
be represented on graphs. Aim of the talk is to present intersections and possible contributions
to Combinatorial Design given by the application of Combinatorial Optimization techniques
and solution methods. This is accomplished by the presentation of results on the Oberwolfach
Problem (OP) where interaction of methods from both domains enabled us to solve large OP
instances in limited computational time and at the same time to derive a theoretical result for
general classes of instances.
On the existence of large set of partitioned incomplete Latin squares
Cong Shen, 2609154311@qq.com
Nanjing Normal University, China
Coauthors: Haitao Cao, Dongliang Li, Li Wang
In this talk, we survey the existence of large sets of partitioned incomplete Latin squares
(LSPILS). Algebraic and combinatorial methods are employed to construct the large sets of
partitioned incomplete Latin squares of type gnu1. Furthermore, we prove that there exists a
pair of orthogonal LSPILS(1pu1)s for any odd u and some even values of u, where p is a prime.
Lastly, we propose some problems for further research.
266
References
[1] D. Crnkovic´, D. Dumicˇic´ Danilovic´, S. Rukavina, Enumeration of symmetric (45,12,3)
designs with nontrivial automorphisms, J. Algebra Comb. Discrete Struct. Appl. 3 (2016),
145–154.
[2] D. Crnkovic´, S. Rukavina, L. Simcˇic´, On triplanes of order twelve admitting an automor-
phism of order six and their binary and ternary codes, Util. Math. 103 (2017), 23–40.
Merging Combinatorial Design and Optimization: the Oberwolfach
Problem
Fabio Salassa, fabio.salassa@polito.it
Politecnico di Torino, Italy
Coauthors: Gabriele Dragotto, Tommaso Traetta, Marco Buratti, Federico Della Croce
Combinatorial optimization is a subset of mathematical optimization that is related to opera-
tions research, algorithm theory, and computational complexity theory. It consists of finding an
(optimal) object from a finite set of objects and in many such problems, exhaustive search is not
tractable. Combinatorial design theory is the part of combinatorial mathematics that deals with
the existence, construction and properties of systems of finite sets whose arrangements satisfy
generalized concepts of balance and/or symmetry. Combinatorial Design and Combinatorial
Optimization, though apparently different research fields, share common problems, such as for
example sudokus, covering arrays, tournament design and more in general problems that can
be represented on graphs. Aim of the talk is to present intersections and possible contributions
to Combinatorial Design given by the application of Combinatorial Optimization techniques
and solution methods. This is accomplished by the presentation of results on the Oberwolfach
Problem (OP) where interaction of methods from both domains enabled us to solve large OP
instances in limited computational time and at the same time to derive a theoretical result for
general classes of instances.
On the existence of large set of partitioned incomplete Latin squares
Cong Shen, 2609154311@qq.com
Nanjing Normal University, China
Coauthors: Haitao Cao, Dongliang Li, Li Wang
In this talk, we survey the existence of large sets of partitioned incomplete Latin squares
(LSPILS). Algebraic and combinatorial methods are employed to construct the large sets of
partitioned incomplete Latin squares of type gnu1. Furthermore, we prove that there exists a
pair of orthogonal LSPILS(1pu1)s for any odd u and some even values of u, where p is a prime.
Lastly, we propose some problems for further research.
266
