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### PhD Exit Seminar: Combinatorial Methods for Barcode Analysis

**Special Events**

Speaker: | Edgar Jaramillo Rodriguez, UC Davis |

Location: | 2112 MSB |

Start time: | Fri, May 26 2023, 2:10PM |

A barcode is a finite multiset of closed intervals on the real line. Barcodes are important objects in topological data analysis, where they serve as summaries of the persistent homology groups of a filtration. We introduce a new combinatorial invariant associated to barcodes by mapping each barcode to a multipermutation, i.e., a permutation of some mul- tiset, which captures the overlapping arrangement of its bars. We call the set all such multipermutations the space of combinatorial barcodes. We define an order on this space and show that the resulting poset is a graded lattice. The cover relations in this lattice can also be used to determine the set of barcode bases of persistence modules. We also explore some connections between combinatorial barcodes, trapezoidal words, and Stirling permutations.

oin Zoom Meeting https://ucdavis.zoom.us/j/92540784489?pwd=SEtMUHorQm01ZzBsdFN3SEdiUzMyZz09 Meeting ID: 925 4078 4489 Passcode: 764777