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arXiv · 1702.06684

Residues modulo powers of two in the Young-Fibonacci lattice

N. Karimilla Bi·Amritanshu Prasad·P. Giftson Santhosh
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Abstract

We study the subgraph of the Young-Fibonacci graph induced by elements with odd $f$-statistic (the $f$-statistic of an element $w$ of a differential graded poset is the number of saturated chains from the minimal element of the poset to $w$). We show that this subgraph is a binary tree. Moreover, the odd residues of the $f$-statistics in a row of this tree equidistibute modulo any power two. This is equivalent to a purely number theoretic result about the equidistribution of residues modulo powers of two among the products of distinct odd numbers less than a fixed number.

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N. Karimilla Bi, Amritanshu Prasad, P. Giftson Santhosh. 2017-02-22. Residues modulo powers of two in the Young-Fibonacci lattice. https://arxiv.org/abs/1702.06684

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