Bibliographic Details
| Title: |
On the number of [formula omitted]-arithmetic expressions in [formula omitted] distinct variables. |
| Authors: |
Stošić, Ivan1 (AUTHOR), Ranđelović, Žarko2,3 (AUTHOR), Damnjanović, Ivan1,4,5,6 (AUTHOR) ivan.damnjanovic@famnit.upr.si |
| Source: |
Discrete Applied Mathematics. Jun2026, Vol. 386, p279-292. 14p. |
| Subjects: |
Arithmetic, Independent variables, Parameterization, Algebraic field theory, Computational complexity, Applied mathematics |
| Abstract: |
How many arithmetic expressions are there in n distinct variables? In this paper, we provide a Θ (n 2) algorithm for computing this number for arithmetic expressions over an arbitrary field F. We consider several cases of this problem with various restrictions on the allowed operations. An expression tree is an ordered rooted tree whose internal nodes represent operations to be performed, while its leaves correspond to formal variables from a set X. We view any arithmetic expression as an element of F (X) that is obtained by evaluating an expression tree. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
