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We derive a new formula for the number of factorizations of a full cycle into an ordered product of two permutations of given cycle types. For the first time, a purely combinatorial argument involving a bijective description of bicolored maps of specified vertex degree distribution is used. All the previous results in the field rely either partially or… (More)

- A Anand, A Villella, L C Ryner, T Carlo, S F Goodwin, H J Song +5 others
- Genetics
- 2001

A multibranched hierarchy of regulatory genes controls all aspects of somatic sexual development in Drosophila melanogaster. One branch of this hierarchy is headed by the fruitless (fru) gene and functions in the central nervous system, where it is necessary for male courtship behavior as well as the differentiation of a male-specific abdominal structure,… (More)

We evaluate combinatorially certain connection coefficients of the symmetric group that count the number of factorizations of a long cycle as a product of three permutations. Such factorizations admit an important topological interpretation in terms of unicellular constellations on orientable surfaces. Algebraic computation of these coefficients was first… (More)

We study the factorizations of the permutation (1, 2,. .. , n) into k factors of given cycle types. Using representation theory, Jackson obtained for each k an elegant formula for counting these factorizations according to the number of cycles of each factor. In the cases k = 2, 3 Schaeffer and Vassilieva gave a combinatorial proof of Jackson's formula, and… (More)

- A Villanueva, J Lozano, A Morales, X Lin, X Deng, M O Hengartner +1 other
- The EMBO journal
- 2001

Although in vitro evidence suggests two c-Jun N-terminal kinase (JNK) kinases, MKK4 and MKK7, transactivate JNK, in vivo confirmation is incomplete. In fact, JNK deficiency may differ from the composite deficiency of MKK4 and MKK7 in Drosophila and mice. Recently, the Caenorhabditis elegans homolog of human JNK, jnk-1, and two MKK-7s, mek-1 and jkk-1, were… (More)

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements 1, 2,. .. , k are in distinct… (More)

This paper is devoted to the evaluation of the generating series of the connection coefficients of the double cosets of the hyperoctahedral group. Hanlon, Stanley, Stembridge (1992) showed that this series, indexed by a partition ν, gives the spectral distribution of some random matrices that are of interest in random matrix theory. We provide an explicit… (More)

We previously observed that glioma cells are differentially sensitive to ABT-737 and, when used as a single-agent, this drug failed to induce apoptosis. Identification of therapeutic strategies to enhance the efficacy of the Bcl-2 inhibitor ABT-737 in human glioma is of interest. Histone deacetylation inhibitors (HDACI) are currently being assessed… (More)

We establish the relationship between volumes of flow polytopes associated to signed graphs and the Kostant partition function. A special case of this relationship, namely, when the graphs are signless, has been studied in detail by Baldoni and Vergne using techniques of residues. In contrast with their approach, we provide combina-torial proofs inspired by… (More)

There are numerous combinatorial objects associated to a Grassmannian permutation w λ that index cells of the totally nonnegative Grassmannian. We study some of these objects (rook placements, acyclic orientations, various restricted fillings) and their q-analogues in the case of permutations w that are not necessarily Grassmannian. Résumé. Il y a nombreaux… (More)