A combinatorial proof of the extension property for partial isometries
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
A note on another construction of graphs with vertices and cyclic automorphism group of order
The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having vertices and automorphism group cyclic of order , . As a special case we get graphs with vertices and cyclic automorphism groups of order . It can revive interest in related problems.
Bergman complexes, Coxeter arrangements, and graph associahedra.
Binary codes and partial permutation decoding sets from the odd graphs
For k ≥ 1, the odd graph denoted by O(k), is the graph with the vertex-set Ωk, the set of all k-subsets of Ω = 1, 2, …, 2k +1, and any two of its vertices u and v constitute an edge [u, v] if and only if u ∩ v = /0. In this paper the binary code generated by the adjacency matrix of O(k) is studied. The automorphism group of the code is determined, and by identifying a suitable information set, a 2-PD-set of the order of k 4 is determined. Lastly, the relationship between the dual code from O(k)...
Categorification of the virtual braid groups
We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.
Cubical convex ear decompositions.
Cyclic sieving for longest reduced words in the hyperoctahedral group.
Distinguishing maps.
Distinguishing number of countable homogeneous relational structures.
Edge-Transitivity of Cayley Graphs Generated by Transpositions
Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn, S) is edge-transitive....
Explicit Cayley covers of Kautz digraphs.
Finitely presented subgroups of systolic groups are systolic
We prove that every finitely presented subgroup of a systolic group is itself systolic.
From a 1-rotational RBIBD to a partitioned difference family.
Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories
The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.
Gröbner basis techniques in algebraic combinatorics.
Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the algebra A of all arithmetic functions, we establish a corresponding subalgebra AG = C*[α(G)]︀ of A. We construct a suitable representation of AG, determined both by G and by an arbitrarily fixed prime p. And then based on this representation, we...
Poset homology of Rees products, and -Eulerian polynomials.
Promotion and evacuation on standard Young tableaux of rectangle and staircase shape.
Some design theoretic results on the Conway group .0.
The centers of gravity of the associahedron and of the permutahedron are the same.