scholarly journals Inversions Within Restricted Fillings of Young Tableaux

10.37236/1030 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Sarah Iveson
Keyword(s):  
Upper Bound ◽  
Exact Expression ◽  
Flag Varieties ◽  
Young Tableaux ◽  
Geometric Properties ◽  
Number Of Components ◽  
Hessenberg Varieties ◽  
Special Cases

In this paper we study inversions within restricted fillings of Young tableaux. These restricted fillings are of interest because they describe geometric properties of certain subvarieties, called Hessenberg varieties, of flag varieties. We give answers and partial answers to some conjectures posed by Tymoczko. In particular, we find the number of components of these varieties, give an upper bound on the dimensions of the varieties, and give an exact expression for the dimension in some special cases. The proofs given are all combinatorial.

scholarly journals The Algebraic Degree of Phase-Type Distributions

2010 ◽  
Vol 47 (03) ◽  
pp. 611-629
Author(s):  
Mark Fackrell ◽  
Qi-Ming He ◽  
Peter Taylor ◽  
Hanqin Zhang
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Polynomial Algorithm ◽  
Algebraic Degree ◽  
Nonnegative Matrices ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
The Matrix

This paper is concerned with properties of the algebraic degree of the Laplace-Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polynomial algorithm, a method for computing the algebraic degree of a PH distribution is developed. The maximum algebraic degree is identified explicitly. Using Perron-Frobenius theory of nonnegative matrices, a lower bound and an upper bound on the minimum algebraic degree are found, subject to some conditions. Explicit results are obtained for special cases.

scholarly journals On connectedness of power graphs of finite groups

2018 ◽  
Vol 17 (10) ◽  
pp. 1850184 ◽  
Author(s):  
Ramesh Prasad Panda ◽  
K. V. Krishna
Keyword(s):  
Finite Groups ◽  
Upper Bound ◽  
The Other ◽  
Number Of Components ◽  
Cyclic Groups ◽  
Power Graph ◽  
Vertex Set ◽  
Proper Power

The power graph of a group [Formula: see text] is the graph whose vertex set is [Formula: see text] and two distinct vertices are adjacent if one is a power of the other. This paper investigates the minimal separating sets of power graphs of finite groups. For power graphs of finite cyclic groups, certain minimal separating sets are obtained. Consequently, a sharp upper bound for their connectivity is supplied. Further, the components of proper power graphs of [Formula: see text]-groups are studied. In particular, the number of components of that of abelian [Formula: see text]-groups are determined.

scholarly journals Geometric Mappings under the Perturbed Extension Operators in Complex Systems Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Chaojun Wang ◽  
Yanyan Cui ◽  
Hao Liu
Keyword(s):  
Complex Systems ◽  
Unit Ball ◽  
Systems Analysis ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Geometric Properties ◽  
Geometric Characteristics ◽  
New Approaches ◽  
Special Cases ◽  
Hartogs Domains

In this paper, we mainly seek conditions on which the geometric properties of subclasses of biholomorphic mappings remain unchanged under the perturbed Roper-Suffridge extension operators. Firstly we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Secondly, applying the analytical characteristics and growth results of subclasses of biholomorphic mappings, we conclude that the generalized Roper-Suffridge operators preserve the geometric properties of strong and almost spiral-like mappings of typeβand orderα,SΩ⁎(β,A,B)as well as almost spiral-like mappings of typeβand orderαunder different conditions on Bergman-Hartogs domains. Sequentially we obtain the conclusions on the unit ballBnand for some special cases. The conclusions include and promote some known results and provide new approaches to construct biholomorphic mappings which have special geometric characteristics in several complex variables.

scholarly journals Study of Second Hankel Determinant for Certain Subclasses of Functions Defined by Al-Oboudi Differential Operator

2020 ◽  
Vol 17 (1(Suppl.)) ◽  
pp. 0353
Author(s):  
K. A. Challab et al.
Keyword(s):  
Differential Operator ◽  
Upper Bound ◽  
Unit Disc ◽  
Hankel Determinant ◽  
Special Cases ◽  
Second Hankel Determinant

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

scholarly journals Branch and Bound Method to Solve Multi Objectives Function

2016 ◽  
Vol 12 (3) ◽  
pp. 5964-5974
Author(s):  
Tahani Jabbar Kahribt ◽  
Mohammed Kadhim Al- Zuwaini
Keyword(s):  
Lower Bounds ◽  
Branch And Bound ◽  
Single Machine ◽  
Upper Bound ◽  
Completion Time ◽  
Heuristic Method ◽  
Total Weighted Completion Time ◽  
Branch And Bound Method ◽  
Special Cases ◽  
Weighted Completion Time

This paper  presents  a  branch  and  bound  algorithm  for  sequencing  a  set  of  n independent  jobs  on  a single  machine  to  minimize sum of the discounted total weighted completion time and maximum lateness,  this problems is NP-hard. Two lower bounds were proposed and heuristic method to get an upper bound. Some special cases were  proved and some dominance rules were suggested and proved, the problem solved with up to 50 jobs.

scholarly journals Prym–Brill–Noether Loci of Special Curves

2020 ◽  
Author(s):  
Steven Creech ◽  
Yoav Len ◽  
Caelan Ritter ◽  
Derek Wu
Keyword(s):  
Upper Bound ◽  
Betti Number ◽  
Young Tableaux

Abstract We use Young tableaux to compute the dimension of $V^r$, the Prym–Brill–Noether locus of a folded chain of loops of any gonality. This tropical result yields a new upper bound on the dimensions of algebraic Prym–Brill–Noether loci. Moreover, we prove that $V^r$ is pure dimensional and connected in codimension $1$ when $\dim V^r \geq 1$. We then compute the 1st Betti number of this locus for even gonality when the dimension is exactly $1$ and compute the cardinality when the locus is finite and the edge lengths are generic.

scholarly journals On the Strong Equitable Vertex 2-Arboricity of Complete Bipartite Graphs

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1778
Author(s):  
Fangyun Tao ◽  
Ting Jin ◽  
Yiyou Tu
Keyword(s):  
Upper Bound ◽  
Maximum Degree ◽  
Bipartite Graphs ◽  
Equitable Partition ◽  
Special Cases ◽  
Vertex Set ◽  
Complete Bipartite Graphs

An equitable partition of a graph G is a partition of the vertex set of G such that the sizes of any two parts differ by at most one. The strong equitable vertexk-arboricity of G, denoted by vak≡(G), is the smallest integer t such that G can be equitably partitioned into t′ induced forests for every t′≥t, where the maximum degree of each induced forest is at most k. In this paper, we provide a general upper bound for va2≡(Kn,n). Exact values are obtained in some special cases.

On norm of single layer potentials on segments

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Seyed M. Zoalroshd
Keyword(s):  
Upper Bound ◽  
Single Layer ◽  
Exact Expression ◽  
Operator Norm ◽  
Equal Length ◽  
Layer Potentials ◽  
Schmidt Norm ◽  
Special Case

AbstractWe show that, for a special case, equality of the spectra of single layer potentials defined on two segments implies that these segments must have equal length. We also provide an upper bound for the operator norm and exact expression for the Hilbert–Schmidt norm of single layer potentials on segments.

scholarly journals Isomorphic subgraphs having minimal intersections

1983 ◽  
Vol 35 (3) ◽  
pp. 287-306
Author(s):  
R. C. Mullin ◽  
B. K. Roy ◽  
P. J. Schellenberg
Keyword(s):  
Complete Graph ◽  
Upper Bound ◽  
Packing Problem ◽  
Finite Graph ◽  
Combinatorial Problems ◽  
Set Packing ◽  
Complete Subgraph ◽  
Special Cases ◽  
Set Packing Problem ◽  
Special Classes

AbstractGiven a finite graph H and G, a subgraph of it, we define σ (G, H) to be the largest integer such that every pair of subgraphs of H, both isomorphic to G, has at least σ(G, H) edges in common; furthermore, R(G, H) is defined to be the maximum number of subgraphs of H, all isomorphic to G, such that any two of them have σ(G, H) edges common between them. We are interested in the values of σ(G, H) and R(G, H) for general H and G. A number of combinatorial problems can be considered as special cases of this question; for example, the classical set-packing problem is equivalent to evaluating R (G, H) where G is a complete subgraph of the complete graph H and σ(G, H) = 0, and the decomposition of H into subgraphs isomorphic to G is equivalent to showing that σ(G, H) = 0 and R(G, H) = ε(H)/ε(G) where ε(H), ε(G) are the number of edges in H, G respectively.A result of S. M. Johnson (1962) gives an upper bound for R(G, H) in terms of σ(G, H). As a corollary of Johnson's result, we obtain the upper bound of McCarthy and van Rees (1977) for the Cordes problem. The remainder of the paper is a study of σ (G, H) and R(G, H) for special classes of graphs; in particular, H is a complete graph and G is, in most instances, a union of disjoint complete subgraphs.

scholarly journals PARABOLIC KAZHDAN–LUSZTIG BASIS, SCHUBERT CLASSES, AND EQUIVARIANT ORIENTED COHOMOLOGY

2019 ◽  
Vol 19 (6) ◽  
pp. 1889-1929
Author(s):  
Cristian Lenart ◽  
Kirill Zainoulline ◽  
Changlong Zhong
Keyword(s):  
Cohomology Ring ◽  
Flag Varieties ◽  
Special Cases ◽  
Oriented Cohomology ◽  
Schubert Classes ◽  
New Interpretation ◽  
The Moment ◽  
The Right ◽  
Relationship Of ◽  
The Relationship

We study the equivariant oriented cohomology ring $\mathtt{h}_{T}(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott–Samelson classes in $\mathtt{h}_{T}(G/P)$ can be obtained by applying this action to the fundamental class of the identity point, hence generalizing previously known results of Chow groups by Brion, Knutson, Peterson, Tymoczko and others. Our main result concerns the equivariant oriented cohomology theory $\mathfrak{h}$ corresponding to the 2-parameter Todd genus. We give a new interpretation of Deodhar’s parabolic Kazhdan–Lusztig basis, i.e., we realize it as some cohomology classes (the parabolic Kazhdan–Lusztig (KL) Schubert classes) in $\mathfrak{h}_{T}(G/P)$. We make a positivity conjecture, and a conjecture about the relationship of such classes with smoothness of Schubert varieties. We also prove the latter in several special cases.

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