排序方式: 共有123条查询结果,搜索用时 31 毫秒
41.
Toufik Mansour 《Discrete Applied Mathematics》2009,157(8):1974-1978
For each permutation π we introduce the variation statistic of π, as the total number of elements on the right between each two adjacent elements of π. We modify this new statistic to get a slightly different variant, which behaves more closely like Mahonian statistics such as maj. In this paper we find an explicit formula for the generating function for the number of permutations of length n according to the variation statistic, and for that according to the modified version. 相似文献
42.
43.
Given a collection of connected graphs one may build bridge and chain graphs out of them. In this paper it is shown how the
Wiener, hyper-Wiener, detour and hyper-detour indices for bridge and chain graphs are determined from the respective indices
of the individual graphs. The results obtained are illustrated by some examples. 相似文献
44.
A well‐known conjecture in topological graph theory says that the genus distribution of every graph is log‐concave. In this paper, the genus distribution of the circular ladder is re‐derived, using overlap matrices and Chebyshev polynomials, which facilitates proof that this genus distribution is log‐concave. 相似文献
45.
A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ? of the rational integers such that ?[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus greater than one. Expecting the converse of the last statement is true, we show some theoretical and experimental results, which support this conjecture. 相似文献
46.
In this paper we present a new combinatorial class enumerated by Catalan numbers. More precisely, we establish a bijection between the set of partitions π1π2?πn of [n] such that πi+1−πi≤1 for all i=,1,2…,n−1, and the set of Dyck paths of semilength n. Moreover, we find an explicit formula for the generating function for the number of partitions π1π2?πn of [n] such that either πi+?−πi≤1 for all i=1,2,…,n−?, or πi+1−πi≤m for all i=1,2,…,n−1. 相似文献
47.
A permutation is said to be alternating if it starts with
rise and then descents and rises come in turn. In this paper we study the generating function for the
number of alternating permutations on n letters that avoid or
contain exactly once 132 and also avoid or contain exactly once an arbitrary pattern on
k letters. In several interesting cases the generating function
depends only on k and is expressed via Chebyshev polynomials of the second kind.AMS Subject Classification: 05A05, 05A15, 30B70, 42C05. 相似文献
48.
We present an explicit formula for the average
-norm over all the polynomials of degree n with coefficients in T, where T is a finite set of complex numbers and α is a positive integer. 相似文献
49.
A class of dynamic control systems described by semilinear fractional stochastic differential equations of order 1 < q < 2 with nonlocal conditions in Hilbert spaces is considered. Using solution operator theory, fractional calculations, fixed-point technique and methods adopted directly from deterministic control problems, a new set of sufficient conditions for nonlocal approximate controllability of semilinear fractional stochastic dynamic systems is formulated and proved by assuming the associated linear system is approximately controllable. As a remark, the conditions for the exact controllability results are obtained. Finally, an example is provided to illustrate the obtained theory. 相似文献
50.
Aubrey Blecher Charlotte Brennan Arnold Knopfmacher Toufik Mansour 《Discrete Mathematics》2017,340(10):2456-2465
We define to be a (totally ordered) alphabet on letters. A word
of length on the alphabet is an element of . A word can be represented by a bargraph (i.e., by a column-convex polyomino whose lower edges lie on the -axis) in which the height of the th column equals the size of the th part of the word. Thus these bargraphs have heights which are less than or equal to . We consider the perimeter, which is the number of edges on the boundary of the bargraph. By way of Cramer’s method and the kernel method, we obtain the generating function that counts the perimeter of words. Using these generating functions we find the average perimeter of words of length over the alphabet . We also show how the mean and variance can be obtained using a direct counting method. 相似文献