منابع مشابه
Enumerating alternating tree families
We study two enumeration problems for up-down alternating trees, i.e., rooted labelled trees T , where the labels v1, v2, v3, . . . on every path starting at the root of T satisfy v1 < v2 > v3 < v4 > · · · . First we consider various tree families of interest in combinatorics (such as unordered, ordered, d-ary and Motzkin trees) and study the number Tn of different up-down alternating labelled ...
متن کاملEnumeration results for alternating tree families
We study two enumeration problems for up-down alternating trees, i.e., rooted labelled trees T , where the labels v1, v2, v3, . . . on every path starting at the root of T satisfy v1 < v2 > v3 < v4 > · · · . First we consider various tree families of interest in combinatorics (such as unordered, ordered, d-ary and Motzkin trees) and study the number Tn of different up-down alternating labelled ...
متن کاملUnknotting Numbers of Alternating Knot and Link Families
After proving a theorem about the general formulae for the signature of alternating knot and link families, we distinguished all families of knots obtained from generating alternating knots with at most 10 crossings and alternating links with at most 9 crossings, for which the unknotting (unlinking) number can be confirmed by using the general formulae for signatures.
متن کاملSome families of Mathieu a-series and alternating Mathieu a-series
The main purpose of this paper is to present a number of potentially useful integral representations for the familiar Mathieu a-series as well as for its alternating version. These results are derived here from many different considerations and are shown to yield sharp bounding inequalities involving the Mathieu and alternating Mathieu a-series. Relationships of the Mathieu a-series with the Ri...
متن کاملPartly occupied Wannier functions.
We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding-antibonding closing procedure. We demonstrate the equivalence between bonding-antibonding closure and the mini...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1972
ISSN: 0021-9045
DOI: 10.1016/0021-9045(72)90045-7