The simple permutations in two permutation classes — the 321-avoiding permutations and the skew-merged permutations — are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards from the enumeration of the class, but the simple permutations had not been enumerated explicitly. In particular, the enumeration of the simple skew-merged permut...

Centrosymmetric involutions in the symmetric group S2n are permutations π such that π = π−1 and π(i) + π(2n + 1 − i) = 2n + 1 for all i, and they are in bijection with involutions of the hyperoctahedral group. We describe the distribution of some natural descent statistics on 321-avoiding centrosymmetric involutions, including the number of descents in the first half of the involution, and the ...

There are at least three di erent bijections in the literature from Dyck paths to 321-avoiding permutations, due to Billey-Jockusch-Stanley, Krattenthaler, and Mansour-Deng-Du. How di erent are they? Denoting them B;K;M respectively, we show that M = B Æ L = K Æ L where L is the classical Kreweras-Lalanne involution on Dyck paths and L0, also an involution, is a sort of derivative of L. Thus K ...

Let Tn be the set of 321-avoiding permutations of order n. Two properties of Tn are proved: (1) The last descent and last index minus one statistics are equidistributed over Tn, and also over subsets of permutations whose inverse has an (almost) prescribed descent set. An analogous result holds for Dyck paths. (2) The sign-and-last-descent enumerators for T2n and T2n+1 are essentially equal to ...

1 Modulating μ-Opioid Receptor Phosphorylation Switches Agonist-Dependent Signaling as Reflected in PKCε Activation and Dendritic Spine Stability Hui Zheng, Ji Chu, Yuhan Zhang, Horace H. Loh and Ping-Yee Law From Department of Pharmacology, University of Minnesota, 6-120 Jackson Hall, 321 Church St. S.E., Minneapolis, Minnesota, 55455-0217, USA. South China Institute for Stem Cell Biology and ...

In (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials Px,w in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where W = Sn (the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic...

Sensitive, high resolution images of the double-double radio galaxy PKS B1545−321 reveal detailed structure, which we interpret in the light of previous work on the interaction of restarted jets with pre-existing relict cocoons. We have also examined the spectral and polarization properties of the source, the color distribution in the optical host and the environment of this galaxy in order to ...

"Critical autoethnography and intercultural learning: emerging voices." Language Intercultural Communication, 21(2), pp. 320–321