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Question Number 186285 by Shrinava last updated on 03/Feb/23

Prove that: R (m , n) ≤ C_(m+n) ^m Here R states the Ramsey theory

Provethat:R(m,n)⩽Cm+nmHereRstatestheRamseytheory

Commented by mr W last updated on 03/Feb/23

R(m,n)≤R(m−1,n)+R(m,n−1) R(m,n)≤ (((m+n−2)),((m−1)) ) = (((n+m−1)),(m) )− (((n+m−2)),(m) ) = (((n+m)),(m) )− (((n+m−1)),((m−1)) )− (((n+m−2)),(m) ) ≤ (((n+m)),(m) )

R(m,n)⩽R(m−1,n)+R(m,n−1)R(m,n)⩽(m+n−2m−1)=(n+m−1m)−(n+m−2m)=(n+mm)−(n+m−1m−1)−(n+m−2m)⩽(n+mm)

Commented by Shrinava last updated on 03/Feb/23

perfect dear professor thank you so much

perfectdearprofessorthankyousomuch

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