Recent special session on geometric and algebraic combinatorics.
European Journal of Combinatorics 43, pp 229–248, 2015. [ journal ] [ arXiv ] [ preprint ]
Dear NSA: Long-Term Security Depends on Freedom.
Notices of the American Math Society, p7, Jan. 2014. [ journal ] [ preprint ] [ G+]
In-depth discussion at the n-cafe, especially here.
Recursive bijections for Catalan objects. (with M. Kafashan, M. Maleki and M. Strayer)
Journal of Integer Sequences, 16, Article 13.5.3, pp 1-20, 2013. [ journal ] [ arXiv ] [ preprint ]
Cofree compositions of coalgebras. (with A. Lauve & F. Sottile)
Annals of Combinatorics, 17(1), pp 105-130, 2013. [ journal ] [ arXiv ] [ preprint ]
When does compromise prevent more pollution?
(with C. Clemons, J. Cossey, M. Ferrara, T. Norfolk, G. Obeng, D. Ricciardi, G. Young)
Notices of the A.M.S, 59(9), pp 1223-1234, 2012. [ journal ] [ arXiv (soon) ] [ preprint ]
Extending the Tamari lattice to some compositions of species.
Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift.,
Progress in Mathematics, Vol. 299, pp 187-210, F. Müller-Hoissen, J. Pallo, J. Marcel, J. Stasheff (Eds.), 2012. [ book ] [ arXiv ] [ preprint ] [ contents ]
Cofree compositions of coalgebras (extended abstract). (with A. Lauve & F. Sottile)
DMTCS Proceedings, FPSAC 23, Reykjavik, Iceland. 363-374, 2011. [ journal ] [ arXiv ] [ preprint ]
Pseudograph associahedra. (with M. Carr & S. Devadoss)
Journal of Combinatorial Theory, Series A 118(7), pp 2035-2055, 2011. [ journal ] [ arXiv ] [ preprint ]
Hopf structures on the multiplihedra. (with A. Lauve & F. Sottile)
SIAM Journal on Discrete Mathematics, 24(4), pp 1250-1271, 2010. [ journal ] [ arXiv ] [ preprint ]
Geometric combinatorial algebras: cyclohedron and simplex. (with D. Springfield)
Journal of Algebraic Combinatorics, 32, pp 597-627, 2010. [ journal ] [ arXiv ] [ preprint ]
New Hopf structures on binary trees. (with A. Lauve & F. Sottile)
DMTCS Proceedings,21st Formal Power Series
and Algebraic Combinatorics (Hagenberg, Austria), pp 411-420 , 2009. [ journal ] [ arXiv ] [ preprint ]
Marked tubes and the graph multiplihedron. (with S.L. Devadoss)
Algebraic and Geometric Topology, 8(4), pp 2081–2108, 2008. [ arXiv ] [ journal ]
Convex Hull Realizations of the Multiplihedra
Topology and its Applications, 156, 326-347, 2008. [ arXiv ] [ journal ]
Quotients of the multiplihedron as categorified associahedra.
Homotopy, Homology and Applications, vol. 10(2), pp 227–256, 2008. [ arXiv ] [ journal ]
Operads in iterated monoidal categories (with J. Siehler, E. Seth Sowers)
Journal of Homotopy and Related Structures, 2, pp 1-43, 2007. [ arXiv ] [ journal ]
Classification of braids which give rise to interchange (with F. Humes)
Algebraic and Geometric Topology, 7, pp 1233-1274, 2007. [ arXiv ] [ journal ]
Vertically iterated classical enrichment
Theory and Applications of Categories, 12, pp 299-325, 2004. [ arXiv ] [ journal ]
Enrichment over iterated monoidal categories
Algebraic and Geometric Topology, 4, pp 95-119, 2004. [ arXiv ] [ journal ]
In brane-world theory, the ends of strings are anchored in our brane, so the particles we see can only move within the brane. But the particles that carry the gravitational force, known as gravitons, are closed strings -- little Cheerios -- and can "leak" out of the brane. This explains why gravity is much weaker than the electromagnetic force and the strong and weak nuclear forces. It also offers a possible explanation for the "dark matter" that astronomers need to explain why the mass of the universe doesn't agree with the observed objects. Dark matter could be in an adjacent brane, with its gravitons leaking into ours.