Abstract
We study the range of the permanent function for the multidimensional matrices of 0 and 1. The main result is a multidimensional versionfor the Brualdi–Newman upper bound on the consecutive values of the permanent (1965).Moreover, we deduce a formula for the permanent of the multidimensional (0,1)-matrices through the number of partial zero diagonals.Using the formula, we evaluate the permanents of the (0,1)-matrices with a few zerosand estimate the permanents of the matrices whose all zero entries are located in several orthogonal hyperplanes.We consider some divisibility properties of the permanent andillustrate the results by studying the values of the permanent for the 3-dimensional (0,1)-matrices of order 3.
| Original language | English |
|---|---|
| Pages (from-to) | 262-276 |
| Number of pages | 15 |
| Journal | Siberian Mathematical Journal |
| Volume | 63 |
| Issue number | 2 |
| DOIs | |
| State | Published - Mar 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, Pleiades Publishing, Ltd.
Keywords
- (0,1)-matrix
- 512.643:519.142
- Brualdi–Newman theorem
- multidimensional matrix
- permanent