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Creators/Authors contains: "Gao, Yibo"

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  1. Abstract We study the ring of regular functions on the space of planar electrical networks, which we coin thegrove algebra. This algebra is an electrical analog of the Plücker ring studied classically in invariant theory. We develop the combinatorics of double groves to study the grove algebra, and find a quadratic Gröbner basis for the grove ideal. 
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  2. Abstract We present a direct bijection between reduced pipe dreams and reduced bumpless pipe dreams (BPDs) by interpreting reduced compatible sequences on BPDs and show that this is the unique bijection preserving bijective realizations of Monk’s formula, establishing its canonical nature. 
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