Abstract:The left and right q-deformed rational numbers were introduced by Bapat, Becker and Licata via regular continued fractions, and they gave a homological interpretation for left and right q-deformed rational numbers. In the present paper, we focus on negative continued fractions and defined left q-deformed negative continued fractions. We give a formula for computing the q-deformed Farey sum of the left q-deformed rational numbers based on it. We use this formula to give a combinatorial proof of the relationship… Show more
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