▫$\mathbb{Z}_2$▫-graded codimensions of unital algebrasRepovš, Dušan (Avtor) Zaicev, Mikhail (Avtor) polynomial identitiesgraded algebrascodimensionsexponential growthWe study polynomial identities of nonassociative algebras constructed by using infinite binary words and their combinatorial properties. Infinite periodic and Sturmian words were first applied for constructing examples of algebras with an arbitrary real PI-exponent greater than one. Later, we used these algebras for a confirmation of the conjecture that PI-exponent increases precisely by one after adjoining an external unit to a given algebra. Here, we prove the same result for these algebras for graded identities and graded PI-exponent, provided that the grading group is cyclic of order two.20182019-09-03 13:13:32Članek v reviji109453UDK: 512.554ISSN pri članku: 0218-1967DOI: 10.1142/S0218196718500224COBISS_ID: 18344281OceCobissID: 1554709sl