Snake Graphs Arising from Groves with an Application in Coding Theory

Snake graphs are connected planar consisting of a finite sequence adjacent tiles (squares) T1,T2,…,Tn. In this case, for 1≤j≤n−1, two consecutive Tj and Tj+1 share exactly one edge, either the edge at east (west) (Tj+1) or north (south) (Tj+1). Finding number perfect matchings associated with given snake graph is most remarkable problems regarding these graphs. It worth noting that such allows bijection between set positive continued fractions. Furthermore, have also been used to find closed formulas cluster variables some algebras solutions Markov equation, which well-known Diophantine equation. Recent results prove give rise string modules over path algebras, connecting research theory representation algebras. This paper uses interaction define Brauer configuration induced by schemes multisets called polygons. Such named configurations. work, polygons admissible words, which, after appropriate transformations, permit us sets binary trees groves. Admissible words generate codes whose energy values can be estimated using Catalan numbers. We include in Python routines compute (i.e., codewords), generated codes, numbers dimensions obtained