Hicas of length .
Higher chain formula proved by combinatorics.
Higher order spreading models
We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy . Each contains all spreading models generated by ℱ-sequences with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.
Higher Schwarzian operators and combinatorics of the Schwarzian derivative.
Higher SPIN alternating sign matrices.
Higher-dimensional cluster combinatorics and representation theory
Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite-dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied. Cyclic polytopes are classical objects of study in convex geometry. In particular, their triangulations have been studied with a view towards generalizing the rich combinatorial structure of triangulations of polygons. In this paper, we demonstrate a connection...
Higher-order Lucas numbers.
Highly connected counterexamples to a conjecture on α-domination
An infinite class of counterexamples is given to a conjecture of Dahme et al. [1] concerning the minimum size of a dominating vertex set that contains at least a prescribed proportion of the neighbors of each vertex not belonging to the set.
Highly Saturated Packings and Reduced Coverings.
Histoires de fichiers
Historická perspektiva konečné matematiky
Histories in path graphs
For a given graph G and a positive integer r the r-path graph, , has for vertices the set of all paths of length r in G. Two vertices are adjacent when the intersection of the corresponding paths forms a path of length r-1, and their union forms either a cycle or a path of length k+1 in G. Let be the k-iteration of r-path graph operator on a connected graph G. Let H be a subgraph of . The k-history is a subgraph of G that is induced by all edges that take part in the recursive definition of...
Hoeffding spaces and Specht modules
It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
Hoeffding spaces and Specht modules
It is proved that each Hoeffding space associated with a random permutation (or, equivalently, with extractions without replacement from a finite population) carries an irreducible representation of the symmetric group, equivalent to a two-block Specht module.
Holes in graphs.
Homogeneous colourings of graphs
A proper vertex -colouring of a graph is called -homogeneous if the number of colours in the neigbourhood of each vertex of equals . We explore basic properties (the existence and the number of used colours) of homogeneous colourings of graphs in general as well as of some specific graph families, in particular planar graphs.
Homogeneous digraphs
Homogeneous permutations.
Homogeneous representations of Khovanov–Lauda Algebras
We construct irreducible graded representations of simply laced Khovanov–Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson–Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.
Homogeneously embedding stratified graphs in stratified graphs
A 2-stratified graph is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of . Two -stratified graphs and are isomorphic if there exists a color-preserving isomorphism from to . A -stratified graph is said to be homogeneously embedded in a -stratified graph if for every vertex of and every vertex of , where and are colored the same, there exists an induced -stratified subgraph of containing and a color-preserving...