Wait: (3,0,1) same as (0,1,3), (2,1,1), (2,2,0), and (1,1,2), and (4,0,0) invalid.

Sat, 02 May 2026 20:44:14 +0000

Understanding Coordinate Symmetry: Why (3,0,1) Equals (0,1,3) and Other Valid Permutations in Digit Basis Systems In number theory and computational mathematics, understanding how coordinate permutations affect numerical representations is crucial—especially when working with digit vectors in multi-base or position-variable systems. A common question that arises among enthusiasts and developers alike is: Is the triple (3,0,1) mathematically equivalent to (0,1,3), (2,1,1), (2,2,0), and (1,1,2), and why is (4,0,0) invalid? ### The Math Behind Coordinate Permutations The key concept here lies in symmetry and permutation within a triplet vector — specifically, in how digit values at positions (hundreds, tens, ones) relate under rearrangement. The coordinate (3,0,1) represents the value 3×100 + 0×10 + 1×1 = 301. Swapping values across positions yields equivalent representations only under valid digit constraints of the numerical system—typically base 10 or base-specific systems.