| Title: | Bollobás set pair inequalities for compositions |
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| Authors: | ID Tian, Anyuan (Author)
ID Wu, Yaokun (Author) |
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| Files: |  AMC_Tian,Wu_2025.pdf (583,73 KB)
MD5: 33963A1B2CBA345C066766403A4692EC
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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: | A d-composition of a set S is an ordered d-tuple (S₁, …, S_d) where S₁, …, S_d are pairwise disjoint subsets of S. If we have a sequence of d-compositions of a finite set and observe certain intersection patterns among parts of different compositions, what are the corresponding arithmetic constraints on the parameters of this sequence? When d = 1, many results in extremal combinatorics address this question. Bollobás set pair inequality is such a classic result for d = 2. In this note, we provide several arithmetic constraints for general d and propose a conjecture as a linear space analogue for one of them. Our study highlights the connection between extremal combinatorics and Young’s lattice of a rectangle. |
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| Keywords: | Katona weight, Lubell weight, partition, shape homomorphism, Young's lattice of a rectangle |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.08.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 23 str. |
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| Numbering: | Vol. 25, no. 4, [article no.] P4.04 |
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| PID: | 20.500.12556/RUP-22018  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3506.7a1 |
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| Publication date in RUP: | 22.10.2025 |
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| Views: | 436 |
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| Downloads: | 14 |
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