{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:45:20Z","timestamp":1780386320420,"version":"3.54.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We investigate the existence of Boolean degree $d$ functions on the Grassmann graph of $k$-spaces in the vector space $\\mathbb{F}_q^n$. For $d=1$ several non-existence and classification results are known, and no non-trivial examples are known for $n \\geq 5$. This paper focusses on providing a list of examples on the case $d=2$ in general dimension and in particular for $(n, k)=(6,3)$ and $(n,k) = (8, 4)$.We also discuss connections to the analysis of Boolean functions, regular sets\/equitable bipartitions\/perfect 2-colorings in graphs, $q$-analogs of designs, and permutation groups. In particular, this represents a natural generalization of Cameron-Liebler line classes.<\/jats:p>","DOI":"10.37236\/11040","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T17:06:09Z","timestamp":1675962369000},"source":"Crossref","is-referenced-by-count":2,"title":["Degree 2 Boolean Functions on Grassmann Graphs"],"prefix":"10.37236","volume":"30","author":[{"given":"Jan","family":"De Beule","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jozefien","family":"D'haeseleer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ferdinand","family":"Ihringer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan","family":"Mannaert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2023,2,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T17:06:10Z","timestamp":1675962370000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i1p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/11040","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,10]]},"article-number":"P1.31"}}