Ilse Fischer

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We show that a graph has an orientation under which every circuit of even length is clockwise odd if and only if the graph contains no subgraph which is, after the contraction of at most one circuit of odd length, an even subdivision of K 2,3. In fact we give a more general characterisation of graphs that have an orientation under which every even circuit(More)
Monotone triangles are certain triangular arrays of integers, which correspond to n × n alternating sign matrices when prescribing (1, 2,. .. , n) as bottom row of the monotone triangle. In this article we define halved monotone triangles, a specialization of which correspond to vertically symmetric alternating sign matrices. We derive an operator formula(More)
We provide a simplified proof of our operator formula for the number of monotone triangles with prescribed bottom row, which enables us to deduce three generalizations of the formula. One of the generalizations concerns a certain weighted enumeration of monotone triangles which specializes to the weighted enumeration of alternating sign matrices with(More)