지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
이용수
초록· 키워드
오류제보하기
Let N0 be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., P(n, l) = {(x1, x2, . . . , xl) ∈ Nl 0 : x1 + x2 + · · · + xl = n}. For any element u = (u1, u2, . . . , ul) ∈ P(n, l), denote its ith-coordinate by u(i), i.e., u(i) = ui.
A family A ⊆ P(n, l) is said to be t-intersecting if |{i : u(i) = v(i)}| ≥ t for all u, v ∈ A. A family A ⊆ P(n, l) is said to be trivially t-intersecting if there is a t-set T of [l] = {1, 2, . . . , l} and elements ys ∈ N0 (s ∈ T) such that A = {u ∈ P(n, l) : u(j) = yj for all j ∈ T}. We prove that given any positive integers l, t with l ≥ 2t + 3, there exists a constant n0(l, t) depending only on l and t, such that for all n ≥ n0(l, t), if A ⊆ P(n, l) is non-trivially t-intersecting, then |A| ≤ (n + l − t − 1 l − t − 1 ) − ( n − 1 l − t − 1) + t.
Moreover, equality holds if and only if there is a t-set T of [l] such that A = [∪ s∈[l]＼T As ∪ {qi : i ∈ T} , where As = {u ∈ P(n, l) : u(j) = 0 for all j ∈ T and u(s) = 0} and qi ∈ P(n, l) with qi(j) = 0 for all j ∈ [l] ＼ {i} and qi(i) = n.
목차
등록된 정보가 없습니다.
참고문헌 (30)
참고문헌 신청
A. Chowdhury / 2010 / Shadows and intersections in vector spaces / J. Combin. Theory Ser. A 117 (8) : 1095 ~ 1106
A. J. W. Hilton / 1967 / Some intersection theorems for systems of finite sets / Quart. J. Math. Oxford (2) 18 : 369 ~ 384
A. J. W. Hilton / 2006 / A graph-theoretical generalisation of Berges analogue of the Erd˝os-Ko-Rado theorem, Trends in Graph Theory / Birkhauser Verlag : 225 ~ 242
C. Bey / 2005 / On cross-intersecting families of sets / Graphs Combin 21 (2) : 161 ~ 168
C. Godsil / 2009 / A new proof of the Erd˝os-Ko-Rado theorem for intersecting families of permutations / European J. Combin 30 (2) : 404 ~ 414
A. J. W. Hilton / 1967 / Some intersection theorems for systems of finite sets / Quart. J. Math. Oxford (2) 18 : 369 ~ 384
A. J. W. Hilton / 2006 / A graph-theoretical generalisation of Berges analogue of the Erd˝os-Ko-Rado theorem, Trends in Graph Theory / Birkhauser Verlag : 225 ~ 242
C. Bey / 2005 / On cross-intersecting families of sets / Graphs Combin 21 (2) : 161 ~ 168
C. Godsil / 2009 / A new proof of the Erd˝os-Ko-Rado theorem for intersecting families of permutations / European J. Combin 30 (2) : 404 ~ 414
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
An Erdos-Ko-Rado theorem for minimal covers
대한수학회보
2017 .01
-
On diversity of certain t-intersecting families
대한수학회보
2020 .01
-
Erd\H os-Ko-Rado type theorems for simplicial complexes via algebraic shifting
대한수학회지
2020 .01
-
On Erd\H os chains in the plane
대한수학회보
2021 .09
-
Symmetry about circles and constant mean curvature surface
한국수학논문집
2017 .01
-
$L^p$ solutions for general time interval multidimensional BSDEs with weak monotonicity and general growth generators
대한수학회논문집
2018 .01
-
한국과학기술연구원의 TOF-ERD 시스템 구축현황
한국분석과학회 학술대회
2017 .05
-
$2$-color Rado number for $x_1 +x_2 +\cdots +x_n=y_1 +y_2=z$
한국수학논문집
2020 .01
-
An examination of the sequence of intersecting lines using FIB/SEM : focused ion beam/scanning electron microscope
한국분석과학회 학술대회
2016 .05
-
BOUNDED CONVERGENCE THEOREMS
대한수학회지
2017 .01
-
A Study on Reduction of Magnet Usage and Cogging Torque throught the Intersect Consequent Model
한국자기학회 학술연구발표회 논문개요집
2023 .05
-
Derivation of some inequalities using the $(p,q)$-th lower order and $(p,q)$-th weak type of entire functions
대한수학회논문집
2016 .01
-
Weak fuzzy equivalence relations and weak fuzzy congruences
한국수학논문집
2017 .01
-
국내 복잡 지형이 권역별 초미세먼지와 구성 성분의 농도에 미치는 영향
한국대기환경학회 학술대회논문집
2021 .10
-
도심 초등학교 교실 내 미세먼지 특성 연구
한국대기환경학회지(국문)
2021 .02
-
미세먼지 화학적 조성변화에 따른 시정악화 장기 변화 특성 규명
한국대기환경학회 학술대회논문집
2021 .10
-
The stability of weak solutions to an anisotropic polytropic infiltration equation
대한수학회지
2021 .09
-
ON BASIC ANALOGUE OF CLASSICAL SUMMATION THEOREMS DUE TO ANDREWS
호남수학학술지
2016 .01
-
A Chemical Analysis of Airborne Particulates at the near Coast Site, Ul-jin Geun Gyungbook
한국환경과학회지
2015 .05
이 논문의 저자 정보
최근 본 자료
댓글(0)
0