The Bidirectional Ballot Polytope
@article{Miller2018TheBB, title={The Bidirectional Ballot Polytope}, author={Steven J. Miller and Carsten Peterson and Carsten Sprunger and Roger Van Peski}, journal={Integers}, year={2018}, volume={18}, pages={A81} }
A bidirectional ballot sequence (BBS) is a finite binary sequence with the property that every prefix and suffix contains strictly more ones than zeros. BBS's were introduced by Zhao, and independently by Bosquet-M{e}lou and Ponty as $(1,1)$-culminating paths. Both sets of authors noted the difficulty in counting these objects, and to date research on bidirectional ballot sequences has been concerned with asymptotics. We introduce a continuous analogue of bidirectional ballot sequences which we…
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