The spiders S(4m+2, 2m, 1) are e-positive

2024/05/08 by Tang, Davion Q. B., Wang, David G. L., Wang, Monica M. Y. · 1 citation
#05E05 05C15 05A20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.04915

Abstract

By using the composition method, we establish the e-positivity of spiders of the form S(4m+2, 2m, 1), which was conjectured by Aliniaeifard, van Willigenburg and Wang. Following the divide-and-conquer strategy, we group one or two e_J-terms that have positive coefficients with each e_I-term that has a negative coefficient, where the compositions J are selected to be obtained by rearranging the parts of I, and show the positivity of the sum of those coefficients. Our main contribution is an explicit construction of the injection.

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