Results 51 to 60 of about 119 (92)

Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2019
Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of ...
Dun Qiu, Jeffrey Remmel
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Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials) [PDF]

Discrete Mathematics & Theoretical Computer Science, 2017
Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Robert A. Proctor, Matthew J. Willis
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On a generalization of derangement polynomials and numbers

Demonstratio Mathematica
In T. Kim, D. S. Kim, and D. V. Dolgy, Probabilistic derangement numbers and polynomials, Math. Comput. Model. Dyn. Syst. 31 (2025), no. 1, 2529188, Kim-Kim defined the probabilistic derangement polynomials and numbers and found some properties of those ...
Yun Sang Jo, Park Jin-Woo
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Fibonacci Cartan and Lucas Cartan numbers

Open Mathematics
This study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers.
Öztürk İskender, Çakır Hasan
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Zeros distribution and interlacing property for certain polynomial sequences

Open Mathematics
In this article, we first prove that the Hankel determinant of order three of the polynomial sequence {Pn(x)=∑k≥0P(n,k)xk}n≥0{\left\{{P}_{n}\left(x)={\sum }_{k\ge 0}P\left(n,k){x}^{k}\right\}}_{n\ge 0} is weakly (Hurwitz) stable, where P(n,k)P\left(n,k ...
Guo Wan-Ming
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Further results on enumeration of perfect matchings of Cartesian product graphs

Open Mathematics
Counting perfect matchings is an interesting and challenging combinatorial task. It has important applications in statistical physics and chemistry. As the general problem is #P-complete, it is usually tackled by randomized heuristics and approximation ...
Wu Tingzeng, Zeng Xiaolin
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Two-sided permutation statistics via symmetric functions

Forum of Mathematics, Sigma
Given a permutation statistic $\operatorname {\mathrm {st}}$ , define its inverse statistic $\operatorname {\mathrm {ist}}$ by . We give a general approach, based on the theory of symmetric functions, for finding the joint distribution of
Ira M. Gessel, Yan Zhuang
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Sequences in overpartitions. [PDF]

Ramanujan J, 2023
Andrews GE, Uncu AK.
europepmc   +1 more source

On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks. [PDF]

Aequ Math, 2022
Wallner M.
europepmc   +1 more source

Pattern Avoidance in Weak Ascent Sequences [PDF]

Discrete Mathematics & Theoretical Computer Science
In this paper, we study pattern avoidance in weak ascent sequences, giving some results for patterns of length 3. This is an analogous study to one given by Duncan and Steingr\'imsson (2011) for ascent sequences. More precisely, we provide systematically
Beáta Bényi, Toufik Mansour, José L. Ramírez   +2 more
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