Rational parking functions and LLT polynomials

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• 作者：Eugene Gorsky^a ; ^b ; ^{egorskiy@math.ucdavis.edu" class="auth_mail" title="E-mail the corresponding author} ; Mikhail Mazin^c ; ^{mmazin@math.ksu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：LLT polynomials ; Simultaneous cores ; Shuffle conjecture
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：140
• 期：Complete
• 页码：123-140
• 全文大小：540 K

文摘

We prove that the combinatorial side of the “Rational Shuffle Conjecture” provides a Schur-positive symmetric polynomial. Furthermore, we prove that the contribution of a given rational Dyck path can be computed as a certain skew LLT polynomial, thus generalizing the result of Haglund, Haiman, Loehr, Remmel and Ulyanov. The corresponding skew diagram is described explicitly in terms of a certain class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516000054&_mathId=si1.gif&_user=111111111&_pii=S0097316516000054&_rdoc=1&_issn=00973165&md5=1b701d9515f1f5d3970ea07738a28768" title="Click to view the MathML source">(m,n)class="mathContainer hidden">class="mathCode">$(m,n)$-core.