# 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…

## 2 Citations

S ep 2 01 7 A GEOMETRIC PERSPECTIVE ON THE MSTD QUESTION

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- 2018

A more sums than differences (MSTD) set A is a subset of Z for which |A + A| > |A − A|. Martin and O’Bryant used probabilistic techniques to prove that a non-vanishing proportion of subsets of {1, .…

A Geometric Perspective on the MSTD Question

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- 2019

Every finite subset of Z can be transformed into an element of I with the same additive behavior, and it is shown that there are no MSTD sets in I consisting of three or fewer intervals, but there are M STD sets for four or more intervals.

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