19 research outputs found

    Cameron-Liebler sets of k-spaces in PG(n,q)

    Get PDF
    Cameron-Liebler sets of k-spaces were introduced recently by Y. Filmus and F. Ihringer. We list several equivalent definitions for these Cameron-Liebler sets, by making a generalization of known results about Cameron-Liebler line sets in PG(n, q) and Cameron-Liebler sets of k-spaces in PG(2k + 1, q). We also present a classification result

    The Cameron-Liebler problem for sets

    Full text link
    Cameron-Liebler line classes and Cameron-Liebler k-classes in PG(2k+1,q) are currently receiving a lot of attention. Links with the Erd\H{o}s-Ko-Rado results in finite projective spaces occurred. We introduce here in this article the similar problem on Cameron-Liebler classes of sets, and solve this problem completely, by making links to the classical Erd\H{o}s-Ko-Rado result on sets. We also present a characterisation theorem for the Cameron-Liebler classes of sets

    Cameron-Liebler sets of k-spaces in PG(n,q)

    Get PDF
    Cameron-Liebler sets of k-spaces were introduced recently in Filmus and Ihringer (J Combin Theory Ser A, 2019). We list several equivalent definitions for these Cameron-Liebler sets, by making a generalization of known results about Cameron-Liebler line sets in PG(n,q) and Cameron-Liebler sets of k-spaces in PG(2k+1,q). We also present some classification results

    Cameron-Liebler sets of k-spaces in PG(n,q)

    Get PDF
    Cameron-Liebler sets of k-spaces were introduced recently by Y. Filmus and F. Ihringer. We list several equivalent definitions for these Cameron-Liebler sets, by making a generalization of known results about Cameron-Liebler line sets in PG(n, q) and Cameron-Liebler sets of k-spaces in PG(2k + 1, q). We also present a classification result

    Cameron-Liebler kk-sets in AG(n,q)\text{AG}(n,q)

    Full text link
    We study Cameron-Liebler kk-sets in the affine geometry, so sets of kk-spaces in AG(n,q)\text{AG}(n, q). This generalizes research on Cameron-Liebler kk-sets in the projective geometry PG(n,q)\text{PG}(n, q). Note that in algebraic combinatorics, Cameron-Liebler kk-sets of AG(n,q)\text{AG}(n, q) correspond to certain equitable bipartitions of the Association scheme of kk-spaces in AG(n,q)\text{AG}(n, q), while in the analysis of Boolean functions, they correspond to Boolean degree 11 functions of AG(n,q)\text{AG}(n, q). We define Cameron-Liebler kk-sets in AG(n,q)\text{AG}(n, q) by intersection properties with kk-spreads and show the equivalence of several definitions. In particular, we investigate the relationship between Cameron-Liebler kk-sets in AG(n,q)\text{AG}(n, q) and PG(n,q)\text{PG}(n, q). As a by-product, we calculate the character table of the association scheme of affine lines. Furthermore, we characterize the smallest examples of Cameron-Liebler kk-sets. This paper focuses on AG(n,q)\text{AG}(n, q) for n>3n > 3, while the case for Cameron-Liebler line classes in AG(3,q)\text{AG}(3, q) was already treated separately

    Equivalent definitions for (degree one) Cameron-Liebler classes of generators in finite classical polar spaces

    Full text link
    In this article, we study degree one Cameron-Liebler sets of generators in all finite classical polar spaces, which is a particular type of a Cameron-Liebler set of generators in this polar space, [9]. These degree one Cameron-Liebler sets are defined similar to the Boolean degree one functions, [15]. We summarize the equivalent definitions for these sets and give a classification result for the degree one Cameron-Liebler sets in the polar spaces W(5,q) and Q(6,q)

    Regular ovoids and Cameron-Liebler sets of generators in polar spaces

    Full text link
    Cameron-Liebler sets of generators in polar spaces were introduced a few years ago as natural generalisations of the Cameron-Liebler sets of subspaces in projective spaces. In this article we present the first two constructions of non-trivial Cameron-Liebler sets of generators in polar spaces. Also regular m-ovoids of k-spaces are introduced as a generalization of m-ovoids of polar spaces. They are used in one of the aforementioned constructions of Cameron-Liebler sets
    corecore