With a wide range of interests in discrete mathematics, two themes can be found in my work:

(1) Combinatorics of partially ordered sets, including questions of dimension and extremal problems for forbidden posets.

(2) Discrete mathematical biology, including computational complexity questions for discrete models of genome rearrangement as well as collaboration with Jordan's bioinformatics lab to develop algorithms for rapid bacterial typing.

### Publications

#### Appeared

**5.** M. Ferrara, W. Kay, L. Kramer, R. Martin, B. Reiniger, H. Smith, and E. Sullivan. “

The saturation number of induced subposets of the Boolean lattice.”

*Discrete Mathematics* 340.10 (2017): 2479-2487.

**4.** H. Smith, L. A. Székely, and H. Wang. "

Eccentricity Sums in Trees,"

*Discrete Applied Mathematics* 207 (2016): 120-131.

**3.** I. Miklós and H. Smith. "

Sampling and counting genomes rearrangement scenarios."

*BMC Bioinformatics*, 16(Suppl 14):S6 (2015).

**2.** H. Smith and L. A. Székely "Some Remarks on Baranyai's Theorem,"

*Congressus Numerantium* 222 (2014): 43-55.

**1.** R. Hammack and H. Smith. "

Zero Divisors among Digraphs,"

*Graphs and Combinatorics* 30.1, (2014): 171-181. (

*Published on-line DOI:10.1007/s00373-012-1248-x*, 2012)

#### Submitted

**8.** M. Ferrara, D. Johnston, S. Loeb, F. Pfender, A. Schulte, H. Smith, E. Sullivan, M. Tait, C. Tompkins. "

On edge-colored saturation problems,"

*Submitted*.

**7.** F. Barrera-Cruz, T. Prag, H. Smith, L. Taylor, and W. T. Trotter. "

Comparing Dushnik-Miller dimension, Boolean dimension, and local dimension,''

*Submitted*.

**6.** B. Bjorkman, G. Cochran, W. Gao, L. Keough, R. Kirsch, M. Phillipson, D. Rorabaugh, H. Smith, and J. Wise. "

k-foldability of words,"

*Submitted*.

**5.** R. Anderson, S. Bai, F. Barrera-Cruz, É. Czabarka, G. Da Lozzo, N. L. F. Hobson, J. C.-H. Lin, A. Mohr, H. C. Smith, L. Székely, and H. Whitlatch. "

Analogies between the crossing number and the tangle crossing number,"

*Submitted*.

**4.** F. Barrera-Cruz, R. Garcia, P. Harris, B. Kubik, H. Smith, S. Talbott, L. Taylor, and W. T. Trotter. "

The graph of critical pairs of a crown,''

*Submitted*.

**3.** F. Barrera-Cruz, S. Felsner, T. Mészáros, P. Micek, H. Smith, L. Taylor, and W. T. Trotter. "

Separating Tree-Chromatic Number from Path-Chromatic Number,''

*Submitted*.

**2.** I. Miklós and H. Smith. "

The computational complexity of calculating partition functions of optimal medians with Hamming distance"

*Submitted*.

**1.** H. Smith, L. A. Székely, H. Wang, and S. Yuan. "

On different 'middle parts' of a tree,"

*Submitted*.

#### In preparation

**2.** J. Kim, R. R. Martin, T. Masařík, W. Shull, H. Smith, A. Uzzell, and Z. Wang. "Local dimension and size,"

*In preparation.*
**1.** H. F. Espitia, A. T. Chande, H. Smith, I. K. Jordan, and L. Rishishwar. "STing: ultrafast sequence typing with in silico aptamers,"

*In preparation*.