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Combinatorics Seminar - Yuval Peled

Yuval Peled
December 6, 2018
10:20AM - 11:15AM
Cockins Hall 240

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Add to Calendar 2018-12-06 10:20:00 2018-12-06 11:15:00 Combinatorics Seminar - Yuval Peled Title: Enumeration and randomized constructions of hypertrees Speaker: Yuval Peled (Courant Institute, New York University) Abstract: Over thirty years ago, Kalai proved a beautiful d-dimensional analog of Cayley's formula for the number of n-vertex trees. Namely, he enumerated d-dimensional hypertrees weighted by the squared size of their (d-1)-dimensional homology group. This, however, does not answer the more basic problem of unweighted enumeration of d-hypertrees, which is our concern here. We analyse a random-greedy construction of d-hypertrees and show it significantly improves the previous known lower bound for their number. Second, we introduce a model of random 1-out d-dimensional complexes, and show that it has a negligible d-dimensional homology with high probability. Cockins Hall 240 Department of Mathematics math@osu.edu America/New_York public

Title: Enumeration and randomized constructions of hypertrees

Speaker: Yuval Peled (Courant Institute, New York University)

Abstract: Over thirty years ago, Kalai proved a beautiful d-dimensional analog of Cayley's formula for the number of n-vertex trees. Namely, he enumerated d-dimensional hypertrees weighted by the squared size of their (d-1)-dimensional homology group. This, however, does not answer the more basic problem of unweighted enumeration of d-hypertrees, which is our concern here. We analyse a random-greedy construction of d-hypertrees and show it significantly improves the previous known lower bound for their number. Second, we introduce a model of random 1-out d-dimensional complexes, and show that it has a negligible d-dimensional homology with high probability.

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