scholarly journals Alternate transition matrices for Brenti's q-symmetric functions and a class of (q,t)-symmetric functions on the hyperoctahedral group

2005 ◽  
Vol 298 (1-3) ◽  
pp. 230-284
Author(s):  
T.M. Langley
Keyword(s):  
Symmetric Functions ◽  
Transition Matrices ◽  
Hyperoctahedral Group

scholarly journals Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Anouk Bergeron-Brlek
Keyword(s):  
Hopf Algebra ◽  
Symmetric Functions ◽  
Commutative Case ◽  
Hyperoctahedral Group ◽  
International Audience ◽  
Shuffle Product

International audience We consider the graded Hopf algebra $NCSym$ of symmetric functions with non-commutative variables, which is analogous to the algebra $Sym$ of the ordinary symmetric functions in commutative variables. We give formulaes for the product and coproduct on some of the analogues of the $Sym$ bases and expressions for a shuffle product on $NCSym$. We also consider the invariants of the hyperoctahedral group in the non-commutative case and a state a few results. Nous considérons l'algèbre de Hopf graduée $NCSym$ des fonctions symétriques en variables non-commutatives, qui est analogue à l'algèbre $Sym$ des fonctions symétriques en variables commutatives. Nous donnons des formules pour le produit et coproduit sur certaines des bases analogues à celles de $Sym$, ainsi qu'une expression pour le produit $\textit{shuffle}$ sur $NCSym$. Nous considérons aussi les invariants du groupe hyperoctaédral dans le cas non-commutatif et énonçons quelques résultats.

scholarly journals Bijective evaluation of the connection coefficients of the double coset algebra

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Alejandro H. Morales ◽  
Ekaterina A. Vassilieva
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Spectral Distribution ◽  
Symmetric Functions ◽  
Matrix Theory ◽  
Double Coset ◽  
Hyperoctahedral Group ◽  
Connection Coefficients ◽  
Generating Series ◽  
International Audience

International audience This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a partition $ν$, gives the spectral distribution of some random matrices that are of interest in random matrix theory. We provide an explicit evaluation of this series when $ν =(n)$ in terms of monomial symmetric functions. Our development relies on an interpretation of the connection coefficients in terms of locally orientable hypermaps and a new bijective construction between partitioned locally orientable hypermaps and some permuted forests. Cet article est dédié à l'évaluation des séries génératrices des coefficients de connexion des classes doubles (cosets) du groupe hyperoctaédral. Hanlon, Stanley, Stembridge (1992) ont montré que ces séries indexées par une partition $ν$ donnent la distribution spectrale de certaines matrices aléatoires jouant un rôle important dans la théorie des matrices aléatoires. Nous fournissons une évaluation explicite de ces séries dans le cas $ν =(n)$ en termes de monômes symétriques. Notre développement est fondé sur une interprétation des coefficients de connexion en termes d'hypercartes localement orientables et sur une nouvelle bijection entre les hypercartes localement orientables partitionnées et certaines forêts permutées.

scholarly journals The combinatorics of transition matrices between the bases of the symmetric functions and the Bn analogues

1996 ◽  
Vol 153 (1-3) ◽  
pp. 3-27 ◽  
Author(s):  
Desiree A. Beck ◽  
Jeffrey B. Remmel ◽  
Tamsen Whitehead
Keyword(s):  
Symmetric Functions ◽  
Transition Matrices

scholarly journals Lyndon Words and Transition Matrices between Elementary, Homogeneous and Monomial Symmetric Functions

10.37236/1044 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Andrius Kulikauskas ◽  
Jeffrey Remmel
Keyword(s):  
Symmetric Function ◽  
Symmetric Functions ◽  
Elementary Symmetric Function ◽  
Transition Matrices ◽  
Elementary Symmetric Functions ◽  
Combinatorial Interpretations ◽  
Lyndon Words

Let $h_\lambda$, $e_\lambda$, and $m_\lambda$ denote the homogeneous symmetric function, the elementary symmetric function and the monomial symmetric function associated with the partition $\lambda$ respectively. We give combinatorial interpretations for the coefficients that arise in expanding $m_\lambda$ in terms of homogeneous symmetric functions and the elementary symmetric functions. Such coefficients are interpreted in terms of certain classes of bi-brick permutations. The theory of Lyndon words is shown to play an important role in our interpretations.

scholarly journals A SUPERCHARACTER TABLE DECOMPOSITION VIA POWER-SUM SYMMETRIC FUNCTIONS

2013 ◽  
Vol 23 (04) ◽  
pp. 763-778 ◽  
Author(s):  
NANTEL BERGERON ◽  
NATHANIEL THIEM
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Triangular Matrix ◽  
Lower Triangular Matrix ◽  
Transition Matrices ◽  
Triangular Matrices ◽  
Power Sum ◽  
Upper Triangular Matrices ◽  
Upper Triangular Matrix ◽  
Lower Triangular

We give an LU-decomposition of the supercharacter table of the group of n × n unipotent upper triangular matrices over 𝔽q, into a lower-triangular matrix with entries in ℤ[q] and an upper-triangular matrix with entries in ℤ[q-1]. To this end, we introduce a q deformation of a new power-sum basis of the Hopf algebra of symmetric functions in noncommuting variables. The decomposition is obtained from the transition matrices between the supercharacter basis, the q-power-sum basis and the superclass basis. This is similar to the decomposition of the character table of the symmetric group Sn given by the transition matrices between Schur functions, monomials and power-sums. We deduce some combinatorial results associated to this decomposition. In particular, we compute the determinant of the supercharacter table.

A novel cryptosystem based on abstract automata and Latin cubes

2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth
Keyword(s):  
Block Cipher ◽  
Finite Automata ◽  
Theoretical Background ◽  
Point Of View ◽  
Theoretical Point ◽  
Transition Matrices ◽  
Encryption And Decryption ◽  
Secret Keys ◽  
Automata Network ◽  
Fully Functioning

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.

Regional household poverty and mobility analysis – a transition probability approach

2020 ◽  
Vol 63 (3) ◽  
pp. 286-302
Author(s):  
Damian Mowczan ◽  
Keyword(s):  
Transition Probability ◽  
General Level ◽  
Transition Matrices ◽  
Equivalent Unit ◽  
Central Statistical ◽  
Per Capita ◽  
Probability Matrices ◽  
General Mobility ◽  
One Year ◽  
The One

The main objective of this paper was to estimate and analyse transition-probability matrices for all 16 of Poland’s NUTS-2 level regions (voivodeship level). The analysis is conducted in terms of the transitions among six expenditure classes (per capita and per equivalent unit), focusing on poverty classes. The period of analysis was two years: 2015 and 2016. The basic aim was to identify both those regions in which the probability of staying in poverty was the highest and the general level of mobility among expenditure classes. The study uses a two-year panel sub-sample of unidentified unit data from the Central Statistical Office (CSO), specifically the data concerning household budget surveys. To account for differences in household size and demographic structure, the study used expenditures per capita and expenditures per equivalent unit simultaneously. To estimate the elements of the transition matrices, a classic maximum-likelihood estimator was used. The analysis used Shorrocks’ and Bartholomew’s mobility indices to assess the general mobility level and the Gini index to assess the inequality level. The results show that the one-year probability of staying in the same poverty class varies among regions and is lower for expenditures per equivalent units. The highest probabilities were identified in Podkarpackie (expenditures per capita) and Opolskie (expenditures per equivalent unit), and the lowest probabilities in Kujawsko-Pomorskie (expenditures per capita) and Małopolskie (expenditures per equivalent unit). The highest level of general mobility was noted in Małopolskie, for both categories of expenditures.

Modeling a random sequence of extremes of loads for fatigue tests under irregular loading

2020 ◽  
pp. 13-19
Author(s):  
N.A. Mahutov ◽  
I.V. Gadolina ◽  
S.G. Lebedinskiy ◽  
E.S. Oganyan ◽  
A.A. Bautin
Keyword(s):  
Random Sequence ◽  
Fatigue Tests ◽  
Linear Hypothesis ◽  
Resource Estimation ◽  
Transition Matrices ◽  
Random Loading ◽  
Markov Transition ◽  
Random Nature ◽  
Irregular Loading ◽  
Markov Transition Matrices

Methods and approaches to tests under random loading are considered, their role is characterized. To ensure the random nature of loading, a modeling method based on Markov transition matrices and real processes recorded in operation is proposed. Keywords: random loading process, Markov repetition matrices, resource estimation, corrected linear hypothesis, parameter of completeness of the loading spectrum. [email protected]

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