排列矩陣的漢克爾、托普利茲序列

Abstract

α是一個由{1, 2, ... , n}中的n個數字所組成的排列，我們把α記為(a_1, a_2, ... , a_n)且對於任意{1, 2, ... , n}中的數字i其?α(i)都會是a_i。排列矩陣M?_α是一個(0,1)-矩陣，其中，當mi,j的j座標等於a_i時其值為1。顯而易見的，以此定義出的M_α?中的每一行、每一列恰好只有一個"1"。漢克爾X射線h(M?_α)和托普利茲X射t(M_α?)，分別用(h_1, h_2, ... , h_2n

Let α be a permutation of {1, 2, ... , n}. We use(a_1, a_2, ... , a_n) to denote α where ?α(i) = a_i for i∈{1, 2, ... , n}.The permutation matrix M?_α is a (0, 1)-matrix such that mi,j = 1 if and only if a_i= j.Clearly, in M?_α, each row and each column contains exactly one "1".The Hankel X-ray h(M?_α) and Toeplitz X-ray t(M?_α) are defi?ned as 2n-1 ordered tuples respectively, (h_1, h_2, ... , h_2n