BibTeX entry
@article{OnPellegrinos20CapsinS43,
key = {OnPellegrinos20CapsinS43},
type = {article},
title = {On Pellegrino's 20-Caps in {\$}S{\_}{\{}4,3{\}}{\$}},
author = {R. Hill},
abstract = {Although Pellegrino demonstrated that every 20-cap in {\$}S{\_}{\{}4,3{\}}{\$} is one of two geometric types, but it is by no means clear how many inequivalent 20-caps are there in each type. This chapter demonstrates that there are in all exactly nine inequivalent 20-caps in {\$}S{\_}{\{}4,3{\}}{\$}. It also shows that just two of these occur as the intersection of a 56-cap in {\$}S{\_}{\{}5,3{\}}{\$} with a hyperplane. Because any 10-cap in {\$}S{\_}{\{}3,3{\}}{\$} is an elliptic quadric and is unique up to equivalence, it follows that any choice of E and V is equivalent to any other. However, for a given choice of E and V, there are 310 different r-caps. The seemingly difficult task of finding how many of these are inequivalent is made relatively simple by using the triple transitivity of the group Aut E on the points of E, together with the uniqueness of the ternary Golay code. The chapter identifies those 20-caps that occur as the intersection of a 56-cap in {\$}S{\_}{\{}5,3{\}}{\$} with a hyperplane and shows that caps of both these types do occur as sections of a 56-cap in {\$}S{\_}{\{}5,3{\}}{\$}.},
comment = {},
date_added = {2016-06-01},
date_published = {1983-12-07},
urls = {http://www.sciencedirect.com/science/article/pii/S030402080873322X,http://www.sciencedirect.com/science/article/pii/S030402080873322X/pdf?md5=d1b75feaabe33b62c6beb656d86a2a7d{\&}pid=1-s2.0-S030402080873322X-main.pdf},
collections = {},
url = {http://www.sciencedirect.com/science/article/pii/S030402080873322X http://www.sciencedirect.com/science/article/pii/S030402080873322X/pdf?md5=d1b75feaabe33b62c6beb656d86a2a7d{\&}pid=1-s2.0-S030402080873322X-main.pdf},
urldate = {2016-06-01},
year = 1983
}