| Title: | Size, diversity, minimum degree, sturdiness, dömdödöm |
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| Authors: | ID Patkós, Balázs (Author) |
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| Files: |  AMC_Patkos_2026.pdf (280,76 KB)
MD5: DB2E073116126E4141BA43267CB2D2EA
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | For a family F of sets and a disjoint pair A, B we let F(A, overline(B)) = F ∈ F: A ⊆ F, B ∩ F = ∅}.The (p,q)-dömdödöm of a family F ⊆ 2[n] is β(p, q)(F)=min {|F(A, overline(B))|:|A|=p,|B|=q, A ∩ B = ∅, A, B ⊆ [n]}. This definition encompasses size, diversity, minimum degree, and sturdiness as special cases. We investigate the maximum possible value β(p, q)(n,k) of β(p, q)(F) over all k-uniform intersecting families F ⊂ 2[n]. We determine the order of magnitude of β(p, q)(n,k) for all fixed p,q,k. We relate the asymptotics of β(p, q)(n,k) to the constant value of β(0, q)(n,q+1) and establish β(p, 1)(n,k)=\binom{n-3-p}{k-2-p} and β(p, 2)(n,k)= 2\binom{n-5}{k-3-p} -\binom{n-7}{k-5-p} if n is large enough. |
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| Keywords: | intersecting families, diversity, minimum degree |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 04.03.2026 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 7 str. |
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| Numbering: | Vol. 26, no. 2, [article no.] P2.07 |
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| PID: | 20.500.12556/RUP-23437  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3528.e84 |
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| Publication date in RUP: | 11.08.2026 |
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| Views: | 113 |
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| Downloads: | 1 |
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