Intersection triangles and block intersection numbers of Steiner systems

1974 ◽  
Vol 139 (2) ◽  
pp. 87-104 ◽  
Author(s):  
Benedict H. Gross
Keyword(s):  
Steiner Systems ◽  
Intersection Numbers ◽  
Block Intersection

scholarly journals On some parametric classifications of quasi-symmetric 2-designs

2015 ◽  
Vol 46 (3) ◽  
pp. 269-280
Author(s):  
Debashis Ghosh ◽  
Lakshmi Kanta Dey
Keyword(s):  
Intersection Numbers ◽  
Block Intersection

Quasi-symmetric $2$-designs with block intersection numbers $x$ and $y$, where $y=x+4$ and $x > 0$ are considered. If $D(v, b, r, k, \lambda; x, y)$ is a quasi-symmetric $2$-design with above condition, then it is shown that the number of such designs is finite, whenever $3\leq x \leq 68$. Moreover, the non-existence of triangle free quasi-symmetric $2$-designs under these parameters is obtained.

Pseudo-Anosov Theory

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Braid Groups ◽  
Intersection Numbers ◽  
Branched Covers ◽  
Algebraic Integers ◽  
Dehn Twists ◽  
Mapping Classes ◽  
Dynamical Properties

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.

scholarly journals Block intersection polynomials

2007 ◽  
Vol 39 (4) ◽  
pp. 559-564 ◽  
Author(s):  
Peter J. Cameron ◽  
Leonard H. Soicher
Keyword(s):  
Block Intersection

Intersection Numbers for Twisted Homology

2004 ◽  
Vol 114 (2) ◽  
Author(s):  
Toyoshi Togi
Keyword(s):  
Intersection Numbers ◽  
Twisted Homology
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