Olivier Bernardi

"The theory of correspondence reaches far deeper
than that of mere numerical congruity with which
it is associated as the substance with the shadow"
James Joseph Sylvester

Preprints:

On the spanning trees of the hypercube and other products of graphs.
Manuscript (pdf). Submitted. Abstract
Counting trees using symmetries. Joint work with Alejandro H. Morales.
Manuscript (pdf). Submitted. Abstract
Separation probabilities for products of permutations. Joint work with Rosena R.X. Du, Alejandro H. Morales and Richard P. Stanley.
Manuscript (pdf). Submitted. Abstract
Bijections and symmetries for the factorizations of the long cycle. Joint work with Alejandro H. Morales.
Manuscript (pdf). Submitted. Abstract

Journal articles:

A Short proof of Rayleigh's Theorem with extensions.
Manuscript (pdf). To appear in The American Mathematical Monthly. Abstract
Unified bijections for maps with prescribed degrees and girth. Joint work with Eric Fusy.
Manuscript (pdf). Journal of Combinatorial Theory - Series A, Vol 119, pp 1351-1387 (2012). Abstract
An analogue of the Harer-Zagier formula for unicellular maps on general surfaces.
Manuscript (pdf). Advances in Applied Mathematics, Vol 48(1), pp 164-180 (2012). Abstract
A bijection for triangulations, quadrangulations, pentagulations, etc. Joint work with Eric Fusy.
Manuscript (pdf). Journal of Combinatorial Theory - Series A, Vol 119(1), pp 218-244 (2012). Abstract
A related extended abstract (with less results) appeared in FPSAC 2010.
Counting colored planar maps: algebraicity results. Joint work with Mireille Bousquet-Mélou.
Manuscript (pdf). Journal of Combinatorial Theory - Series B, Vol 101(1), pp 315-377 (2011). Abstract
Schnyder decompositions for regular plane graphs and application to drawing. Joint work with Eric Fusy.
Manuscript (pdf). Algorithmica Vol 62(3), pp 1159-1197 (2012) . Abstract
A bijection for covered maps, or a shortcut between Harer-Zagier's and Jackson's formulas. Joint work with Guillaume Chapuy.
Manuscript (pdf). Journal of Combinatorial Theory - Series A, Vol 118(6), pp 1718-1748 (2011). Abstract
Counting unicellular maps on non-orientable surfaces. Joint work with Guillaume Chapuy.
Manuscript (pdf). Advances in Applied Mathematics Vol 47, pp. 259-275 (2011). Abstract
An extended abstract also appeared in FPSAC 2010.
Enumerating simplicial decompositions of surfaces with boundaries. Joint work with Juanjo Rué.
Manuscript (pdf). European Journal of Combinatorics, Vol 33, pp. 302-325 (2012). Abstract
A linear algorithm for the random sampling from regular languages. Joint work with Omer Gimenez.
Manuscript (pdf). Algorithmica Vol 62(1), pp 130-145 (2012). Abstract
Growth constants of minor-closed classes of graphs. Joint work with Marc Noy and Dominic Welsh.
Manuscript (pdf). Journal of Combinatorial Theory - Series B, Vol 100(5), pp 468-484 (2010). Abstract
A earlier unpublished manuscript (pdf). (It contains less results on factorial classes, but more on sub-factorial classes.) Abstract
A Bijection between well-labelled positive paths and matchings. Joint work with Bertrand Duplantier and Philippe Nadeau.
Manuscript (pdf). Seminaire Lotharingien de Combinatoire, Vol 63, B63e (13 pages) (2010). Abstract
Intervals in Catalan lattices and realizers of triangulations. Joint work with Nicolas Bonichon.
Manuscript (pdf). Journal of Combinatorial Theory - Series A, Vol 116(1), pp 55-75 (2009). Abstract
An extended abstract also appeared in FPSAC 2007.
Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals.
Manuscript (pdf). Seminaire Lotharingien de Combinatoire, Vol 59, B59e (10 pages) (2008). Abstract
Tutte polynomial, subgraphs, orientations and sandpile model: new connections via embeddings.
Manuscript (pdf). Electronic Journal of Combinatorics, Vol 15(1), R109 (52 pages) (2008). Abstract
A characterization of the Tutte polynomial via combinatorial embedding.
Manuscript (pdf). Annals of Combinatorics, Vol 12(2), pp 139-153 (2008). Abstract
On triangulations with high vertex degree.
Manuscript (pdf). Annals of Combinatorics, Vol 12(1), pp 17-44 (2008). Abstract
A related extended abstract also appeared in FPSAC 2005.
Bijective counting of tree-rooted maps and shuffles of parenthesis systems.
Manuscript (pdf). Electronic Journal of Combinatorics, Vol 14, R9 (36 pages) (2007). Abstract
Bijective counting of Kreweras walks and loopless triangulations.
Manuscript (pdf). Journal of Combinatorial Theory - Series A, Vol 114(5), pp 931-956 (2007). Abstract
An related extended abstract also appeared in FPSAC 2006.

Thesis and reports:

Combinatorics of maps and the Tutte polynomial.
Ph.D. dissertation (2006). Supervised by Mireille Bousquet-Mélou.
Comptage des triangulations coloriées .
Master thesis (2003). Supervised by Mireille Bousquet-Mélou.
Reverse engineering of gene regulatory networks.
Internal report, New York University (2002). Supervised by Dennis Shasha.
Design of fault tolerant permutation networks for satellites.
Internal report, INRIA Sophia-Antipolis (2001). Supervised by Jean-Claude Bermond.