Heap (mathematics)
In abstract algebra, a semiheap is an algebraic structure consisting of a non-empty set H with a ternary operation denoted [ x , y , z ] ∈ H {\displaystyle [x,y,z]\in H} that satisfies a modified associativity property: ∀ a , b , c , d , e ∈ H [ [ a , b , c ] , d , e ] = [ a , [ d , c , b ] , e ] = [ a , b , [ c , d , e ] ] . {\displaystyle \forall a,b,c,d,e\in H\quad [[a,b,c],d,e]=[a,[d,c,b],e]=[a,b,[c,d,e]].} A biunitary element h of a semiheap satisfies [h,h,k] = k = [k,h,h] for every k in H. A heap is a semiheap in which every element is biunitary.