The research demonstrates a new formula for m-ary increasing trees in relation to complete graphs, suggesting deeper combinatorial connections.
The number of binary increasing trees is the number of alternating permutations. Riordan found the formulas for the number of ternary and quaternary increasing trees. We obtain an explicit formula for the number of m-ary increasing trees for any m, which can be expressed in terms of the degree-chromatic polynomial of the complete graph.
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Medet Jumadildayev (2025) studied this question.
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