Bollobás set pair inequalities for compositionsTian, Anyuan (Avtor) Wu, Yaokun (Avtor) Katona weightLubell weightpartitionshape homomorphismYoung's lattice of a rectangleA 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.Založba Univerze na Primorskem20252025-10-22 22:00:09Članek v reviji22018sl