Major indices and perfect bases for complex reflection groups.
Majority choosability of 1-planar digraph
A majority coloring of a digraph with colors is an assignment such that for every we have for at most half of all out-neighbors . A digraph is majority -choosable if for any assignment of lists of colors of size to the vertices, there is a majority coloring of from these lists. We prove that if is a 1-planar graph without a 4-cycle, then is majority 3-choosable. And we also prove that every NIC-planar digraph is majority 3-choosable.
Malý výlet do moderní matematiky [Book]
Many Triangulated Spheres.
Map genus, forbidden maps, and monadic second-order logic.
Mapping directed networks.
Mappings of Acyclic and Parking Functions.
Maps on surfaces and Galois groups
Marginalization in models generated by compositional expressions
In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.
Mario Ouellette's arborescent decomposition for species of structures. (Décomposition arborescente de Mario Ouellette pour les espèces de structures.)
Mark sequences in digraphs.
Markov chain small-world model with asymmetric transition probabilities.
Markov convexity and local rigidity of distorted metrics
It is shown that a Banach space admits an equivalent norm whose modulus of uniform convexity has power-type if and only if it is Markov -convex. Counterexamples are constructed to natural questions related to isomorphic uniform convexity of metric spaces, showing in particular that tree metrics fail to have the dichotomy property.
Markov product of positive definite kernels and applications to Q-matrices of graph products
We show positivity of the Q-matrix of four kinds of graph products: direct product (Cartesian product), star product, comb product, and free product. During the discussion we give an alternative simple proof of the Markov product theorem on positive definite kernels.
Matchings and partial patterns.
Matchings and total domination subdivision number in graphs with few induced 4-cycles
A set S of vertices of a graph G = (V,E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γₜ(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Favaron, Karami, Khoeilar and Sheikholeslami (Journal of Combinatorial...
Matchings avoiding partial patterns.
Matchings avoiding partial patterns and lattice paths.
Matchings in complete bipartite graphs and the -Lah numbers
We give a graph theoretic interpretation of -Lah numbers, namely, we show that the -Lah number counting the number of -partitions of an -element set into ordered blocks is just equal to the number of matchings consisting of edges in the complete bipartite graph with partite sets of cardinality and (, ). We present five independent proofs including a direct, bijective one. Finally, we close our work with a similar result for -Stirling numbers of the second kind.
Matchings in hexagonal cacti.