# Fractional cross intersecting families

Let A={A_1,...,A_p} and B={B_1,...,B_q} be two families of subsets of [n] such that for every i∈ [p] and j∈ [q], |A_i∩ B_j|= c/d|B_j|, where c/d∈ [0,1] is an irreducible fraction. We call such families "c/d-cross intersecting families". In this paper, we find a tight upper bound for the product |A||B| and characterize the cases when this bound is achieved for c/d=1/2. Also, we find a tight upper bound on |A||B| when B is k-uniform and characterize, for all c/d, the cases when this bound is achieved.

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research
03/11/2018

### Fractional L-intersecting families

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### Modular and fractional L-intersecting families of vector spaces

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### Quadratically Tight Relations for Randomized Query Complexity

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### r-wise fractional L-intersecting family

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### Doubly transitive equiangular tight frames that contain regular simplices

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### A tight upper bound on the number of non-zero weights of a constacyclic code

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06/29/2016

### Tighter bounds lead to improved classifiers

The standard approach to supervised classification involves the minimiza...