Permanents of Hessenberg (0, 1)-matrices
نویسندگان
چکیده
Let P (m,n) denote the maximum permanent of an n-by-n lower Hessenberg (0, 1)-matrix with m entries equal to 1. A “staircased” structure for some matrices achieving this maximum is obtained, and recursive formulas for computing P (m,n) are given. This structure and results about permanents are used to determine the exact values of P (m,n) for n ≤ m ≤ 8n/3 and for all nnz(Hn) − nnz(Hbn/2c) ≤ m ≤ nnz(Hn), where nnz(Hn) = (n2 + 3n − 2)/2 is the maximum number of ones in an n-by-n Hessenberg (0, 1)-matrix.
منابع مشابه
Determinants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
متن کاملOn the sum of Pell and Jacobsthal numbers by matrix method
In this paper, we define two $n$-square upper Hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph. We investigate relations between permanents and determinants of these upper Hessenberg matrices, and sum formulas of the well-known Pell and Jacobsthal sequences. Finally, we present two Maple 13 procedures in order to calculate permanents of t...
متن کاملOn The Generalized Fibonacci And Pell Sequences By Hessenberg Matrices
In this paper, we consider the generalized Fibonacci and Pell Sequences and then show the relationships between the generalized Fibonacci and Pell sequences, and the Hessenberg permanents and determinants. 1. Introduction The Fibonacci sequence, fFng ; is de ned by the recurrence relation, for n 1 Fn+1 = Fn + Fn 1 (1.1) where F0 = 0; F1 = 1: The Pell Sequence, fPng ; is de ned by the recurrence...
متن کاملOn the Number of 1-factors of Bipartite Graphs
Abstract: In this paper, we investigated relationships between the Fibonacci, Lucas, Padovan numbers and 1-factors of some bipartite graphs with upper Hessenberg adjacency matrix. We calculated permanent of these upper Hessenberg matrices by contraction method and show that their permanents are equal to elements of the Fibonacci, Lucas and Padovan numbers. At the end of the paper, we give some ...
متن کاملOn The Usual Fibonacci and Generalized Order-k Pell Numbers
In this paper, we give some relations involving the usual Fibonacci and generalized order-k Pell numbers. These relations show that the generalized order-k Pell numbers can be expressed as the summation of the usual Fibonacci numbers. We nd families of Hessenberg matrices such that the permanents of these matrices are the usual Fibonacci numbers, F2i 1; and their sums. Also extending these mat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 12 شماره
صفحات -
تاریخ انتشار 2005