## Publications of Jeremy L. Martin

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#### Research publications

1. Simplicial effective resistance and enumeration of spanning trees (with Art M. Duval, Woong Kook, and Kang-Ju Lee)
Preprint (6/6/22). [PDF | arXiv:2206.02182]
2. Hopf monoids of set families (with Kevin Marshall)
Preprint (5/12/22). [PDF | arXiv:2205.05772]
3. Ehrhart theory of paving and panhandle matroids (with Derek Hanely, Daniel McGinnis, Dane Miyata, George D. Nasr, Andrés R. Vindas-Meléndez, and Mei Yin)
Preprint (1/31/22). [PDF | arXiv:2201.12442]
4. Hopf monoids of ordered simplicial complexes (with Federico Castillo and José A. Samper)
Preprint (11/23/20). [PDF | arXiv:2011.14955]
5. Interval parking functions (with Emma Colaric, Ryan DeMuse, and Mei Yin)
Adv. Appl. Math. 123 (2021) 102129. [PDF | arXiv:2006.09321]
6. A positivity phenomenon in Elser's Gaussian-cluster percolation model (with Galen Dorpalen-Barry, Cyrus Hettle, David C. Livingston, George Nasr, Julianne Vega, and Hays Whitlatch)
J. Combin. Theory Ser. A 179 (2021) 105364. [PDF | arXiv:1905.11330]
7. Enumerating parking completions using Join and Split (with Ayomikun Adeniran, Steve Butler, Galen Dorpalen-Barry, Pamela E. Harris, Cyrus Hettle, Qingzhong Liang, and Hayan Nam)
Electron. J. Combin. 27, no. 2 (2020), #P2.44.
8. Increasing spanning forests in graphs and simplicial complexes (with Joshua Hallam and Bruce E. Sagan)
Europ. J. Combin. 76 (2019), 178-198. [PDF | arXiv:1610.05093]
9. Counting arithmetical structures on paths and cycles (with Benjamin Braun, Hugo Corrales, Scott Corry, Luis David García Puente, Darren Glass, Nathan Kaplan, Gregg Musiker, and Carlos E. Valencia)
Discrete Math. 341 (2018), 2949-2963. [PDF | arXiv:1701.06377]
10. A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes (with Ghodratollah Aalipour, Art M. Duval, Woong Kook and Kang-Ju Lee)
J. Combin. Theory Ser. A 158 (2018), 362-386. [PDF | arXiv:1510.00033]
11. Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions (with Vera Mikyoung Hur and Mathew A. Johnson)
Discrete Anal. 2017, Paper No. 13, 20 pp. [PDF | arxiv:1609.02189]
12. Simplicial and Cellular Trees (with Art M. Duval and Caroline J. Klivans)
Recent Trends in Combinatorics (A. Beveridge, J. Griggs, L. Hogben, G. Musiker and P. Tetali, eds.), 713--752, IMA Vol. Math. Appl. 159, Springer, 2016 [PDF | arXiv:1506.06819]
13. A non-partitionable Cohen-Macaulay simplicial complex (with Art M. Duval, Bennet Goeckner and Caroline J. Klivans)
Adv. Math. 299 (2016), 381-395. [PDF | arXiv:1504.04279]
14. Pseudodeterminants and perfect square spanning tree counts (with Molly Maxwell, Victor Reiner, and Scott O. Wilson)
J. Comb. 6, no. 3 (2015), 295-325. [PDF | arXiv:1311.6686]
15. On the spectra of simplicial rook graphs (with Jennifer D. Wagner)
Graphs Combin. 31, no. 5 (2015), 1589-1611. [PDF | arXiv:1209.3493]
16. Cuts and flows of cell complexes (with Art M. Duval and Caroline J. Klivans)
J. Alg. Combin. 41 (2015), 969--999. [PDF | arXiv:1206.6157]
17. Enumerating colorings, tensions and flows in cell complexes (with Matthias Beck, Felix Breuer and Logan Godkin)
J. Combin. Theory Ser. A 122 (2014), 82-106. [PDF | arXiv:1212.6539]
18. Critical groups of simplicial complexes (with Art M. Duval and Caroline J. Klivans)
Ann. Comb. 17 (2013), 53-70; [PDF | arXiv:1101.3981]
19. Graph varieties in high dimension (with Thomas Enkosky)
Beitr. Algebra Geom. 54, no. 1 (2013), 1-12. [PDF | arXiv:1006.5864]
20. The incidence Hopf algebra of graphs (with Brandon Humpert)
SIAM J. Discrete Math. 26, no. 2 (2012), 555-570. [Published version | PDF | arXiv:1012.4786]
21. Cellular spanning trees and Laplacians of cubical complexes (with Art M. Duval and Caroline J. Klivans)
Adv. Appl. Math. 46 (2011), 247-274. [PDF | arXiv:0908.1956]
22. Are node-based and stem-based clades equivalent? Insights from graph theory (with David C. Blackburn and Edward O. Wiley)
PLOS Currents: Tree of Life, article published online 11/18/2010. Full text also available at PubMed Central.
23. Updown numbers and the initial monomials of the slope variety (with Jennifer D. Wagner)
Electronic J. Combin. 16, no. 1 (2009), Research Paper R82. [PDF | arXiv]
24. Simplicial matrix-tree theorems (with Art M. Duval and Caroline J. Klivans)
Trans. Amer. Math. Soc. 361 (2009), no. 11, 6073-6114. [Published version | PDF preprint | arXiv]
25. On distinguishing trees by their chromatic symmetric functions (with Matthew Morin and Jennifer D. Wagner)
J. Combin. Theory Ser. A 115 (2008), 237-253. [PDF | arXiv]
26. Random geometric graph diameter in the unit ball (with Robert B. Ellis and Catherine Yan)
Algorithmica 47, no. 4 (2007), 421-438. [PDF | arXiv]
27. Harmonic algebraic curves and noncrossing partitions (with David Savitt and Ted Singer)
Discrete Comput. Geom. 37, no. 2 (2007), 267-286. [PDF | arXiv]
28. Classification of Ding's Schubert varieties: finer rook equivalence (with Mike Develin and Victor Reiner)
Canad. J. Math. 59, no. 1 (2007), 36-62. [PDF | arXiv]
29. Rigidity theory for matroids (with Mike Develin and Victor Reiner)
Comment. Math. Helv. 82 (2007), 197-233. [PDF | arXiv]
30. The Mathieu group $$M_{12}$$ and the $$M_{13}$$ game (with Noam D. Elkies and John H. Conway)
Experimental Math. 15, no. 2 (2006), 223-236. [PDF | arXiv]
31. The slopes determined by n points in the plane
Duke Math. J. 131, no. 1 (2006), 119-165. [PDF | arXiv]
32. Cyclotomic and simplicial matroids (with Victor Reiner)
Israel J. Math. 150 (2005), 229-240. [PDF | arXiv]
33. On the topology of graph picture spaces
Adv. Math. 191, no. 2 (2005), 312-338. [PDF | arXiv]
34. Factorizations of some weighted spanning tree enumerators (with Victor Reiner)
J. Combin. Theory Ser. A 104, no. 2 (2003), 287-300. [PDF | arXiv]
35. Geometry of graph varieties
Trans. Amer. Math. Soc. 355 (2003), 4151-4169. [PDF | arXiv]
36. Ruling out (160,54,18) difference sets in some nonabelian groups (with Jason Alexander, Rajalakshmi Balasubramanian, Kimberly Monahan, Harriet Pollatsek, and Ashna Rubina Sen)
J. Combin. Designs 8 (2000), no. 4, 221-231. [PDF]

#### Expository articles

1. The Partitionability Conjecture (with Art M. Duval and Caroline J. Klivans)
Notices Amer. Math. Soc. 64, no. 2 (2017), 117-122.

#### Articles in conference proceedings

1. Random geometric graph diameter in the unit disk with $$l_p$$ metric (Extended Abstract) (with Robert B. Ellis and Catherine Yan)
Proceedings of the 12th International Symposium on Graph Drawing (New York, October, 2004), Lecture Notes in Computer Science 3383 (2005), 167-172.

#### Book reviews

1. Review of How to Bake $$\pi$$ by Eugenia Cheng (Basic Books, 2016)
Notices Amer. Math. Soc. 63, no. 9 (2016), 1053-1054.
2. Review of Euler's Gem by David S. Richeson (Princeton U. Press, 2008)
Notices Amer. Math. Soc. 57, no. 11 (2010), 1448-1450.
3. Review of The Cult of Pythagoras by Alberto A. Martínez (U. Pittsburgh Press, 2012)
The Mathematical Intelligencer 35, no. 4 (2013), 81-82.

#### Theses

1. Graph Varieties, Ph.D. thesis, University of California, San Diego, 2002. Advisor: Mark Haiman. [PDF]
2. The Mathieu Group $$M_{12}$$ and Conway's $$M_{13}$$-Game, A.B. thesis, Harvard University, 1996. Advisor: Noam D. Elkies. [PDF]