Matches in SemOpenAlex for { <https://semopenalex.org/work/W3016159905> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W3016159905 abstract "This paper is divided into two logical parts. In the first part of this paper, we prove the following theorem which is the $q$-analogue of a generalized modular Ray-Chaudhuri-Wilson Theorem shown in [Alon, Babai, Suzuki, J. Combin. Theory Series A, 1991]. It is also a generalization of the main theorem in [Frankl and Graham, European J. Combin. 1985] under certain circumstances. 
 $bullet$ Let $V$ be a vector space of dimension $n$ over a finite field of size $q$. Let $K = {k_1, ldots , k_r},L = {mu_1, ldots , mu_s}$ be two disjoint subsets of ${0,1, ldots , b-1}$ with $k_1 < cdots < k_r$. Let $mathcal{F} = {V_1,V_2,ldots,V_m}$ be a family of subspaces of $V$ such that (a) for every $i in [m]$, dim($V_i$) $bmod~ b = k_t$, for some $k_t in K$, and (b) for every distinct $i,j in [m]$, dim($V_i cap V_j$)$bmod~ b = mu_t$, for some $mu_t in L$. Moreover, it is given that neither of the following two conditions hold: 
 
 $q+1$ is a power of 2, and $b=2$
 $q=2, b=6$.
 
 Then,
 $|mathcal{F}| leqslant begin{cases}N(n,s,r,q), & textrm{ if }left(s+k_r leqslant n textrm { and } r(s-r+1) leqslant b-1right) textrm{ or } (s < k_1 + r) N(n,s,r,q) + sum_{t in [r]}left[begin{matrix} n k end{matrix} right]_{q}, & textrm{otherwise,} end{cases}$
 where $N(n,s,r,q) := left[begin{matrix} n s end{matrix} right]_{q} + left[begin{matrix} n s-1 end{matrix} right]_{q} + cdots + left[begin{matrix} n s-r+1 end{matrix} right]_{q}.$ 
 In the second part of this paper, we prove $q$-analogues of results on a recent notion called fractional $L$-intersecting family of sets for families of subspaces of a given vector space over a finite field of size $q$. We use the above theorem to obtain a general upper bound to the cardinality of such families. We give an improvement to this general upper bound in certain special cases." @default.
- W3016159905 created "2020-04-17" @default.
- W3016159905 creator A5065846321 @default.
- W3016159905 creator A5076736694 @default.
- W3016159905 creator A5083947704 @default.
- W3016159905 creator A5090095198 @default.
- W3016159905 date "2022-03-01" @default.
- W3016159905 modified "2023-09-25" @default.
- W3016159905 title "Modular and Fractional $L$-Intersecting Families of Vector Spaces" @default.
- W3016159905 cites W1898703922 @default.
- W3016159905 cites W1986908956 @default.
- W3016159905 cites W2012908763 @default.
- W3016159905 cites W2019935404 @default.
- W3016159905 cites W2064197162 @default.
- W3016159905 cites W2066230934 @default.
- W3016159905 cites W2120888988 @default.
- W3016159905 cites W2794144215 @default.
- W3016159905 cites W3000266334 @default.
- W3016159905 doi "https://doi.org/10.37236/10358" @default.
- W3016159905 hasPublicationYear "2022" @default.
- W3016159905 type Work @default.
- W3016159905 sameAs 3016159905 @default.
- W3016159905 citedByCount "1" @default.
- W3016159905 countsByYear W30161599052023 @default.
- W3016159905 crossrefType "journal-article" @default.
- W3016159905 hasAuthorship W3016159905A5065846321 @default.
- W3016159905 hasAuthorship W3016159905A5076736694 @default.
- W3016159905 hasAuthorship W3016159905A5083947704 @default.
- W3016159905 hasAuthorship W3016159905A5090095198 @default.
- W3016159905 hasBestOaLocation W30161599051 @default.
- W3016159905 hasConcept C114614502 @default.
- W3016159905 hasConcept C12362212 @default.
- W3016159905 hasConcept C13336665 @default.
- W3016159905 hasConcept C2524010 @default.
- W3016159905 hasConcept C33676613 @default.
- W3016159905 hasConcept C33923547 @default.
- W3016159905 hasConcept C45340560 @default.
- W3016159905 hasConcept C7655956 @default.
- W3016159905 hasConcept C77926391 @default.
- W3016159905 hasConceptScore W3016159905C114614502 @default.
- W3016159905 hasConceptScore W3016159905C12362212 @default.
- W3016159905 hasConceptScore W3016159905C13336665 @default.
- W3016159905 hasConceptScore W3016159905C2524010 @default.
- W3016159905 hasConceptScore W3016159905C33676613 @default.
- W3016159905 hasConceptScore W3016159905C33923547 @default.
- W3016159905 hasConceptScore W3016159905C45340560 @default.
- W3016159905 hasConceptScore W3016159905C7655956 @default.
- W3016159905 hasConceptScore W3016159905C77926391 @default.
- W3016159905 hasIssue "1" @default.
- W3016159905 hasLocation W30161599051 @default.
- W3016159905 hasLocation W30161599052 @default.
- W3016159905 hasLocation W30161599053 @default.
- W3016159905 hasOpenAccess W3016159905 @default.
- W3016159905 hasPrimaryLocation W30161599051 @default.
- W3016159905 hasRelatedWork W2009214945 @default.
- W3016159905 hasRelatedWork W2025394619 @default.
- W3016159905 hasRelatedWork W2774077212 @default.
- W3016159905 hasRelatedWork W2952668525 @default.
- W3016159905 hasRelatedWork W2973318292 @default.
- W3016159905 hasRelatedWork W3024615404 @default.
- W3016159905 hasRelatedWork W3081328890 @default.
- W3016159905 hasRelatedWork W3210795967 @default.
- W3016159905 hasRelatedWork W4300802656 @default.
- W3016159905 hasRelatedWork W4321148338 @default.
- W3016159905 hasVolume "29" @default.
- W3016159905 isParatext "false" @default.
- W3016159905 isRetracted "false" @default.
- W3016159905 magId "3016159905" @default.
- W3016159905 workType "article" @default.