Search results for "Combinatorics"
showing 10 items of 1770 documents
Degrees of irreducible characters of the symmetric group and exponential growth
2015
We consider sequences of degrees of ordinary irreducible S n S_n - characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of n n with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound.
Uniformization with infinitesimally metric measures
2019
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb R^2$, whose definition involves deforming lengths of curves by $\mu$. We show that if $\mu$ is an infinitesimally metric measure, i.e., it satisfies an infinitesimal version of the metric doubling measure condition of David and Semmes, then such a $\mu$-quasiconformal map exists. We apply this result to give a characterization of the metric spaces admitting an infinitesimally quasisymmetric parametrization.
Nb 4 Te 17 I 4 , a New Pseudo One‐Dimensional Solid‐State Polytelluride
1994
The new ternary compound Nb4Te17I4 has been prepared and structurally characterized. It crystallizes in the monoclinic system, space group C2/c with unit-cell parameters a = 16.199(4), b = 8.128(2), c = 27.355(6) A, β = 110.84(2)°, Z = 4. The structure consists of infinite one-dimensional niobium/tellurium chains running parallel to the crystallographic c direction. The chains are separated by iodine atoms. Short and long metal–metal distances alternate in the sequence of three consecutive short bonds ([d ≈ 3.1 – 3.2 A) and one long (d = 4.268 A) metal–metal separation. Each Nb atom is eight-coordinate. The composition of the chain is ∞11[(Nb5+)2(Nb4+)2(Te22−)4(Te32−)3(I−)4].
Neighbor-Distinguishing k-tuple Edge-Colorings of Graphs
2009
AbstractThis paper studies proper k-tuple edge-colorings of graphs that distinguish neighboring vertices by their sets of colors. Minimum numbers of colors for such colorings are determined for cycles, complete graphs and complete bipartite graphs. A variation in which the color sets assigned to edges have to form cyclic intervals is also studied and similar results are given.
Permutability of injectors with a central socle in a finite solvable group
2017
In response to an Open Question of Doerk and Hawkes [5, IX Section 3, page 615], we shall show that if Zπ is the Fitting class formed by the finite solvable groups whose π-socle is central (where π is a set of prime numbers), then the Zπ-injectors of a finite solvable group G permute with the members of a Sylow basis in G. The proof depends on the properties of certain extraspecial groups [4].
Pseudocomplements in sum-ordered partial semirings
2007
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings – those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.
A class of generalised finite T-groups
2011
Let F be a formation (of finite groups) containing all nilpotent groups such that any normal subgroup of any T-group in F and any subgroup of any soluble T-group in F belongs to F. A subgroup M of a finite group G is said to be F-normal in G if G/CoreG(M) belongs to F. Named after Kegel, a subgroup U of a finite group G is called a K- F-subnormal subgroup of G if either U=G or U=U0?U1???Un=G such that Ui?1 is either normal in Ui or Ui1 is F-normal in Ui, for i=1,2,...,n. We call a finite group G a TF-group if every K- F-subnormal subgroup of G is normal in G. When F is the class of all finite nilpotent groups, the TF-groups are precisely the T-groups. The aim of this paper is to analyse the…
Injectors with a central socle in a finite solvable group
2013
Abstract In response to an Open Question of Doerk and Hawkes (1992) [2, IX §4, p. 628] , we shall describe three constructions for the Z π -injectors of a finite solvable group, where Z π is the Fitting class formed by the finite solvable groups whose π -socle is central (and π is a set of prime numbers).
A class of imprimitive groups
2010
We classify imprimitive groups inducing the alternating group A4 on the set of blocks, with the inertia subgroup satisfying some very natural geometrical conditions which force the group to operate linearly.
Overlapping self-affine sets of Kakeya type
2009
We compute the Minkowski dimension for a family of self-affine sets on the plane. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.