منابع مشابه
On Cayley's formula for counting trees in nested interval graphs
In this paper it is shown that the spectrum of a nested interval graph has a very simple structure. From this result a formula is derived to the number of spanning trees in a nested interval graph; this is a generalization of the Cayley formula.
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A stabilized-interval-free (SIF) permutation on [n] = {1, 2, ..., n} is one that does not stabilize any proper subinterval of [n]. By presenting a decomposition of an arbitrary permutation into a list of SIF permutations, we show that the generating function A(x) for SIF permutations satisfies the defining property: [xn−1]A(x)n = n! . We also give an efficient recurrence for counting SIF permut...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1982
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1982-0662044-8