交替子群中下降和超越枚举数的同步性

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-07 DOI:10.1016/j.disc.2025.114521

Umesh Shankar

引用次数: 0

摘要

推广Dey[2]的工作，定义了实数序列的超共时性概念。设Bn、k、Cn、k、Pn、k、Qn、k分别为[n]有k个递减的偶排列个数、有k个递减的奇排列个数、有k个递减的偶排列个数和有k个递减的奇排列个数。结果表明，对于所有n≥5的序列，这四个序列都是超同步的。这证明了deybbb的两个猜想得到了加强。

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Synchronicity of descent and excedance enumerators in the alternating subgroup

Generalising the work of Dey [2], we define the notion of ultra-synchronicity of sequences of real numbers. Let

B_{n, k}, C_{n, k}, P_{n, k}, Q_{n, k}

be the number of even permutations of

[n]

with k descents, odd permutations with k descents, even permutations with k excedances and odd permutations with k excedances, respectively. We show that the four sequences are ultra-synchronised for all

n \geq 5

. This proves a strengthening of two conjectures of Dey [2].

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.