Associated event: The First Russian-Japanese mini-workshop on Algebraic combinatorics was held on 29 th and 30 thof August 2016 at Sobolev Institute of Mathematics. (back)
10:00-10:50 Denis Krotov, Trades in combinatorial configurations. (talk)
Abstract. Trades reflect hypothetical differences between two different configurations of the same type (designs, subspace designs, perfect codes, MDS codes, MRD codes, latin squares and hypercubes, etc). In many cases, good lower bounds on the number of configurations are based on switching small trades. The problem of finding trades of minimum size (for given parameters) is often connected to the problem of finding minimum eigenfunction supports of the graph.
11:00-11:20 Inoue Yuhei, The four color theorem and Thompson's F and links. (talk)
Abstract. The four color theorem is known as a theorem whose proof is very long. Bowlin and Brin tried to obtain a shorter proof of the theorem using binary trees with colorings and an infinite group known as Thompson's F in 2013. There is a relationship between the four color theorem and the group. In addition, it is known that we can make a link from an element of the group. We considered relationship between links and elements of Thompson's F with colorings and proved that we can make all of links with elements of Thompson's F and colorings. In this talk, we will introduce the relationship between the four color theorem and Thompson's F, and our results.
11:30-11:50 Olga Parshina, Perfect colorings of infinite circulant graphs with a continuous set of distances (joint work with M. Lisitsyna).
Abstract. We present some results on the perfect colorings (or equitable partitions) of a graph C∞(1,2,3,...,n) ,n∈Z +, which is the Cayley graph of Z with the set of generators (1,2,3,...,n). (This is a joint work with M. Lisitsyna.)
12:00-12:20 Anastasia Vasil'eva, On the eigenfunctions of H(n,q): generalized weight distributions and eigenfunctions.
12:30-12:50 Keiji Ito, Minimum skew energy of tournaments.
Abstract. Adiga, Balakrishnan and So defined skew energy of digraphs in 2010 and gave upper and lower bound for skew energy. A digraph is called a tournament if the underlying graph of the digraph is an undirected complete graph. Tournaments have some common properties. In this talk, we improve the minimum skew energy for tournaments. Moreover, we introduce a generalized concept of skew energy.
13:00-13:20 Konstantin Vorobev, Embedding of eigenfunctions of Johnson graphs into eigenfunctions of hypercubes.
Abstract. We consider a connection between eigenfunctions of the Johnson and Hamming graphs. An eigenfunction of a graph is an eigenvector with a given eigenvalue of its adjacency matrix. We find a criterion for embedding of the Johnson graph's J(n,w) eigenfunction with a given eigenvalue in a certain Hamming graph's eigenfunction with a given eigenvalue.
10:00-10:20 Sho Kubota, A method for getting new switching partitions from old ones.
Abstract. Godsil-McKay switching is often used to construct cospectral graphs. However, we have to prepare a partition of the vertex set that satisfies two very strong conditions to apply switching. We call this partition Godsil-McKay partition. As we see in G2S2 conference, the orbit partition of a group of automorphisms is an equitable partition, so it is sometimes a Godsil-McKay partition. In this talk, we introduce a method for getting new Godsil-McKay partitions from old ones, its algorithm and some results.
10:30-10:50 Aleksandr Valuzhenich, Minimum supports of eigenfunctions of Hamming graphs. (talk)
Abstract. We find the minimum Hamming weight of an eigenfunction of the Hamming graph H(n;q) corresponding to the eigenvalue n(q-1)-q. Moreover, we describe the set of the eigenfunctions with the minimum Hamming weight.
11:00-11:20 Evgeny Bespalov, MDS codes with distance at least 3 in Doob graphs. (talk)
Abstract. The Doob graph D(m,n), where m>0, is the Cartesian product of m copies of the Shrikhande graph and n copies of the complete graph K4 on 4 vertices. The Doob graph D(m,n) is a distance-regular graph with the same parameters as the Hamming graph H(2m+n,4). We characterize MDS codes in Doob graphs with code distance at least 3. Up to equivalence, there exist
m 3/36+7m 2/24+11m/12+1-(m mod 2)/8-(m mod 3)/9)
MDS codes with code distance 2m+n in D(m,n) . Besides that, there are only two MDS codes with code distance 3 in (each of) D(2,0), D(2,1) and with code distance 4 in D(2,1) and one code with code distance 3 in D(1,2), D(1,3) and code distance 4 in D(1,3), D(2,2) , up to equivalence.
11:00-11:20 Ev Sotnikova, Eigenfunctions supports of minimal cardinality for some families of graphs. (talk)
Abstract. This talk is devoted to the problem of finding the eigenfunction supports of minimal cardinality. Stating from the necessary definitions and some intuitive examples we move to the main object of our interest, matrix rank distance graphs. We provide the construction of minimal eigensupports, corresponding to the smallest eigenvalue, for the case of 2×2 matrices over the finite field Fp and discuss the open problems in general case.
The information about Conference Venue was updated.
A guide and a map on places and services that might be helpful during your stay in Akademgorodok contains informations about restaurants, shopping centers, pharmacies, post office, laundary, taxi, currency exchange.
Basketball and volleyball competitions will be held on August, 18th and 25th, from 8pm to 10pm in the NSU Sports Complex. It is also planned that a soccer game will be held on the morning on August, 22nd. If you wish to participate in these sports activities please email us at firstname.lastname@example.org.
The Council of the European Mathematical Society voted on the organisers of the European Congress of Mathematics 2020 and it supported the bid from Slovenia. The European Congress of Mathematics 2020 will be held in Portoroz. Our congratulations!
For more details please visit: link.
All G2S2-participants with accommodation at the NSU Guesthouse will be provided by a wired internet by reguest.
Please email us at email@example.com your MAC address until 01.08.2016.
Abstract submission is closed. We have received 96 abstracts, and 75 of them have been accepted. Thanks to all authors of abstracts!
Registration is closed. We have 138 registered participants. Thanks to all registered participants!
G2S2 is supported by the Russian Foundation for Basic Research, Project 16-31-10290.
Related events: The international workshop «Algorithmic problems in group theory
and related areas» will take place from July 25 till August 5, 2016, in the Novosibirsk region.
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