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Principal specializations of Schubert polynomials and pattern containment
European Journal of Combinatorics ( IF 1 ) Pub Date : 2020-12-17 , DOI: 10.1016/j.ejc.2020.103291 Yibo Gao
中文翻译:
Schubert多项式的主要专业和模式包含
更新日期:2020-12-17
European Journal of Combinatorics ( IF 1 ) Pub Date : 2020-12-17 , DOI: 10.1016/j.ejc.2020.103291 Yibo Gao
The principal specialization of the Schubert polynomial at , which equals the degree of the matrix Schubert variety corresponding to , has attracted a lot of attention in recent years. In this paper, we show that is bounded below by where is the number of occurrences of the pattern in , strengthening a previous result by A. Weigandt. We then make a conjecture relating the principal specialization of Schubert polynomials to pattern containment. Finally, we characterize permutations whose RC-graphs are connected by simple ladder moves via pattern avoidance.
中文翻译:
Schubert多项式的主要专业和模式包含
主要专业 的舒伯特多项式 ,等于矩阵Schubert的度数对应于 ,近年来引起了很多关注。在本文中,我们表明 受以下限制 哪里 是模式的出现次数 在 ,加强了A. Weigandt的先前结果。然后我们进行一个猜想,将Schubert多项式的主要专业性与模式包含性联系起来。最后,我们描述排列 通过模式回避,通过简单的梯形运动将其RC图连接起来。