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Almost entropic matroids and (k,L)-systems
Abstract
For an integer k and a set of integers L, a (k,L)-system is a family of k-element sets such that the size of the intersection of any two distinct members belongs to L. Let m(n,k,L) denote the maximum size of a (k,L)-system on a ground set of n elements. In this work, we establish a close connection between the asymptotic growth of m(n,k,L) and almost entropic matroids. As a consequence, we obtain a general computable upper bound on the asymptotics of m(n,k,L) that unifies and strengthens all previously known upper bounds.
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BibTeX
@misc{kupavskii2026almost,
title = {{Almost entropic matroids and $(k,L)$-systems}},
author = {Andrey Kupavskii and Nikolai Terekhov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27892},
eprint = {2610.27892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27892},
}
RIS
TY - UNPB
TI - Almost entropic matroids and (k,L)-systems
AU - Andrey Kupavskii
AU - Nikolai Terekhov
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27892
UR - https://arxiv.org/abs/2610.27892
AB - For an integer k and a set of integers L, a (k,L)-system is a family of k-element sets such that the size of the intersection of any two distinct members belongs to L. Let m(n,k,L) denote the maximum size of a (k,L)-system on a ground set of n elements. In this work, we establish a close connection between the asymptotic growth of m(n,k,L) and almost entropic matroids. As a consequence, we obtain a general computable upper bound on the asymptotics of m(n,k,L) that unifies and strengthens all previously known upper bounds.
ER -