منابع مشابه
Permutation statistics on involutions
In this paper we look at polynomials arising from statistics on the classes of involutions, In, and involutions with no fixed points, Jn, in the symmetric group. Our results are motivated by F. Brenti’s conjecture [3] which states that the Eulerian distribution of In is logconcave. Symmetry of the generating functions is shown for the statistics d, maj and the joint distribution (d, maj). We sh...
متن کاملA Statistic on Involutions
We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I (n)denote the set of all involutions on [n](= {1, 2, . . . , n}) and let F(2n)denote the set of all fixed point free involutions on [2n]. For an involution δ, let |δ| denote the number of 2-cycles in δ. Let [n]q = 1+q+· · ·+qn−1 and let (k)q denote the q-binomial coefficient....
متن کاملInvolutions on Generating Functions
We study a family of involutions on the space of sequences. Many arithmetically or combinatorially interesting sequences appear as eigensequences of the involutions. We develop new tools for studying sequences using these involutions.
متن کاملInvolutions on Baxter Objects
Baxter numbers are known to count several families of combinatorial objects, all of which come equipped with natural involutions. In this paper, we add a combinatorial family to the list, and show that the known bijections between these objects respect these involutions. We also give a formula for the number of objects fixed under this involution, showing that it is an instance of Stembridge’s ...
متن کاملInvolutions on Spin 4-manifolds
We show that a simply-connected spin 4-manifold which admits a locally linear involution must have vanishing signature. We also show that the codimensions of all components of the fixed point set of an involution on a spin 4-manifold are the same modulo 4 . There is no assumption of local linearity in this result, which extends a lemma of Atiyah and Bott. This note records two results about inv...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics
سال: 1967
ISSN: 0022-4340
DOI: 10.6028/jres.071b.004