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### How to show Well Founded Induction false? [closed]

The abstract reduction system ({a,b,c,d},→) where the → is defined as:
http://i.stack.imgur.com/TS0Ud.png
Let Q be a monadic predicate on {a,b,c,d} such that Q(a) = Q(b) = false and Q(c) = Q(d) = ...

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### reduction to np hard ordering problem

I am trying to show a reduction from a problem of ordering problem to an np-hard problem that has approximation poly-time algorithm.
My problem is: I have M auctions and in each auction I have N ...

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### Minimum number of edges - directed graph with given sums of weights

Let's consider a directed graph with positive edge weights. For every vertex we determine the difference
D = (summary weight of edges directed FROM this vertex)-(summary weight of edges directed ...

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### Relating the toric rank of a semistable curve and the first Betti number of its reduction graph

Introduction
Let $k$ be a local field. Let $C$ be the spectrum of $\mathcal{O}_{k}$. Let $X/k$ be a smooth projective curve with a semistable model $\mathcal{X}/C$.
Let $J$ be the Jacobian of $X$. ...