Some new results in the combinatorial theory of rings and groups

1988 ◽  
pp. 34-43
Author(s):  
L. A. Bokut
Keyword(s):  
Combinatorial Theory

scholarly journals A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path

2012 ◽  
Vol 64 (4) ◽  
pp. 822-844 ◽  
Author(s):  
J. Haglund ◽  
J. Morse ◽  
M. Zabrocki
Keyword(s):  
Building Blocks ◽  
Main Diagonal ◽  
Combinatorial Theory ◽  
Dyck Path ◽  
Dyck Paths ◽  
Littlewood Polynomials ◽  
Diagonal Harmonics ◽  
Littlewood Polynomial ◽  
Theory Operator ◽  
Shuffle Conjecture

Abstract We introduce a q, t-enumeration of Dyck paths that are forced to touch the main diagonal at specific points and forbidden to touch elsewhere and conjecture that it describes the action of the Macdonald theory ∇ operator applied to a Hall–Littlewood polynomial. Our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the “shuffle conjecture” (Duke J. Math. 126 (2005), pp. 195 − 232) for ∇ en[X]. We bring to light that certain generalized Hall–Littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of q, t-Catalan sequences, and we prove a number of identities involving these functions.

Projective planes of infinite but isolic order

1976 ◽  
Vol 41 (2) ◽  
pp. 391-404 ◽  
Author(s):  
J. C. E. Dekker
Keyword(s):  
Projective Plane ◽  
Finite Projective Plane ◽  
Projective Planes ◽  
Latin Squares ◽  
Combinatorial Theory ◽  
Ternary Ring ◽  
Orthogonal Latin Squares ◽  
Mutually Orthogonal Latin Squares ◽  
Planar Ternary Ring ◽  
Partial Recursive Functions

The main purpose of this paper is to show how partial recursive functions and isols can be used to generalize the following three well-known theorems of combinatorial theory.(I) For every finite projective plane Π there is a unique number n such that Π has exactly n2 + n + 1 points and exactly n2 + n + 1 lines.(II) Every finite projective plane of order n can be coordinatized by a finite planar ternary ring of order n. Conversely, every finite planar ternary ring of order n coordinatizes a finite projective plane of order n.(III) There exists a finite projective plane of order n if and only if there exist n − 1 mutually orthogonal Latin squares of order n.

scholarly journals A Combinatorial Theory of Higher-Dimensional Permutation Arrays

2000 ◽  
Vol 25 (2) ◽  
pp. 194-211 ◽  
Author(s):  
Kimmo Eriksson ◽  
Svante Linusson
Keyword(s):  
Combinatorial Theory ◽  
Permutation Arrays ◽  
Higher Dimensional

On the Foundation of Combinatorial Theory. X. A Categorical Setting for Symmetric Functions

1992 ◽  
Vol 86 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Flavio Bonetti ◽  
Gian-Carlo Rota ◽  
Domenico Senato ◽  
Antonietta M. Venezia
Keyword(s):  
Symmetric Functions ◽  
Combinatorial Theory ◽  
Categorical Setting ◽  
Theory X

Quantum algebras and parity-dependent spectra

2007 ◽  
Vol 463 (2086) ◽  
pp. 2415-2427 ◽  
Author(s):  
C.V Sukumar ◽  
Andrew Hodges
Keyword(s):  
Quantum Optics ◽  
Harmonic Oscillator ◽  
Combinatorial Theory ◽  
Squeezed States ◽  
Quantum Algebras ◽  
Matrix Elements ◽  
Euler Numbers ◽  
Simple Harmonic Oscillator ◽  
Non Gaussian ◽  
Special Case

We study the structure of a quantum algebra in which a parity-violating term modifies the standard commutation relation between the creation and annihilation operators of the simple harmonic oscillator. We discuss several useful applications of the modified algebra. We show that the Bernoulli and Euler numbers arise naturally in a special case. We also show a connection with Gaussian and non-Gaussian squeezed states of the simple harmonic oscillator. Such states have been considered in quantum optics. The combinatorial theory of Bernoulli and Euler numbers is developed and used to calculate matrix elements for squeezed states.

Insertion-Duplication Mutagenesis inStreptococcus pneumoniae: Targeting Fragment Length Is a Critical Parameter in Use as a Random Insertion Tool

1998 ◽  
Vol 64 (12) ◽  
pp. 4796-4802 ◽  
Author(s):  
Myeong S. Lee ◽  
Chaok Seok ◽  
Donald A. Morrison
Keyword(s):  
Gene Knockout ◽  
Genomic Analysis ◽  
Combinatorial Theory ◽  
Donor Plasmid ◽  
Uniform Size ◽  
Knock Out ◽  
Duplication Events ◽  
Simplifying Assumptions ◽  
Insertion Tool ◽  
Random Insertion

ABSTRACT To examine whether insertion-duplication mutagenesis with chimeric DNA as a transformation donor could be valuable as a gene knockout tool for genomic analysis in Streptococcus pneumoniae, we studied the transformation efficiency and targeting specificity of the process by using a nonreplicative vector with homologous targeting inserts of various sizes. Insertional recombination was very specific in targeting homologous sites. While the recombination rate did not depend on which site or region was targeted, it did depend strongly on the size of the targeting insert in the donor plasmid, in proportion to the fifth power of its length for inserts of 100 to 500 bp. The dependence of insertion-duplication events on the length of the targeting homology was quite different from that for linear allele replacement and places certain limits on the design of mutagenesis experiments. The number of independent pneumococcal targeting fragments of uniform size required to knock out any desired fraction of the genes in a model genome with a defined probability was calculated from these data by using a combinatorial theory with simplifying assumptions. The results show that efficient and thorough mutagenesis of a large part of the pneumococcal genome should be practical when using insertion-duplication mutagenesis.

A combinatorial theory of minimal social situations

1992 ◽  
Vol 17 (2-3) ◽  
pp. 105-125 ◽  
Author(s):  
Tadeusz Sozański
Keyword(s):  
Combinatorial Theory ◽  
Social Situations
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