2021/03/16 by Cossidente, Antonio, Marino, Giuseppe, Pavese, Francesco +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2103.09336
Let \cal P be a finite classical polar space of rank d. An m-regular system with respect to (k - 1)-dimensional projective spaces of \cal P, 1 ≤ k ≤ d - 1, is a set \cal R of generators of \cal P with the property that every (k - 1)-dimensional projective space of \cal P lies on exactly m generators of \cal R. Regular systems of polar spaces are investigated. Some non-existence results about certain 1-regular systems of polar spaces with low rank are proved and a procedure to obtain m'-regular systems from a given m-regular system is described. Finally, three different construction methods of regular systems w.r.t. points of various polar spaces are discussed.