Yeong-Nan Yeh
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Yeong-Nan Yeh has a total of 61 co-authors. Here are the top co-authors by number of shared publications:
- Shi-Mei Ma
School of Mathematics and Statistics Shandong University of Technology 255000 Zibo Shandong P.R. China
33 shared publications - Jun Ma
Shanghai Jiao Tong University
19 shared publications - Jean Yeh
Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
13 shared publications - Toufik Mansour
University of Haifa
5 shared publications - Weigen Yan
School of Science, Jimei University, Xiamen, China
5 shared publications Shi-Mei Ma
3 shared publications
Latest Publications
- Open Access
Symmetric decompositions and Euler-Stirling statistics on Stirling permutations
The Stirling permutations introduced by Gessel-Stanley have recently received considerable attention. Motivated by Ji's work on $(α,β)$-Eulerian polynomials (Sci China Math., 2025) and Yan-Yang-Lin's work on $1/k$-Eulerian polynomials (J. Combin. Theory Ser. A, 2026), we present several symmetric decompositions of the enumerators related to Euler-Stirling statistics on Stirling permutations. Firstly, we provide a partial symmetric decomposition for the $1/k$-Eulerian polynomial. Secondly, we give several unexpected applications of the $(p,q)$-Eulerian polynomials, where $p$ marks the number of fixed points of permutations and $q$ marks that of cycles. From this paper, one can see that $(p,q)$-Eulerian polynomial contains a great deal of information about permutations and Stirling permutations. Using the change of grammars, we show that the $(α,β)$-Eulerian polynomials introduced by Carlitz-Scoville can be deduced from the $(p,q)$-Eulerian polynomials by special parametrizations. We then introduce proper and improper ascent-plateau statistics on Stirling permutations. Moreover, we introduce proper ascent, improper ascent, proper descent and improper descent statistics on permutations. Furthermore, we consider the joint distributions of Euler-Stirling statistics on permutations, including the numbers of improper ascents, proper ascents, left-to-right minima and right-to-left minina. In the final part, we first give a symmetric decomposition of the joint distribution of the ascent-plateau and left ascent-plateau statistics, and then we show that the $q$-ascent-plateau polynomials are bi-$γ$-positive, where $q$ marks the number of left-to-right minima.Open AccessSymmetric decompositions and Euler-Stirling statistics on Stirling permutations
The Stirling permutations introduced by Gessel-Stanley have recently received considerable attention. Motivated by Ji's work on $(α,β)$-Eulerian polynomials (Sci China Math., 2025) and Yan-Yang-Lin's work on $1/k$-Eulerian polynomials (J. Combin. Theory Ser. A, 2026), we present several symmetric decompositions of the enumerators related to Euler-Stirling statistics on Stirling permutations. Firstly, we provide a partial symmetric decomposition for the $1/k$-Eulerian polynomial. Secondly, we give several unexpected applications of the $(p,q)$-Eulerian polynomials, where $p$ marks the number of fixed points of permutations and $q$ marks that of cycles. From this paper, one can see that $(p,q)$-Eulerian polynomial contains a great deal of information about permutations and Stirling permutations. Using the change of grammars, we show that the $(α,β)$-Eulerian polynomials introduced by Carlitz-Scoville can be deduced from the $(p,q)$-Eulerian polynomials by special parametrizations. We then introduce proper and improper ascent-plateau statistics on Stirling permutations. Moreover, we introduce proper ascent, improper ascent, proper descent and improper descent statistics on permutations. Furthermore, we consider the joint distributions of Euler-Stirling statistics on permutations, including the numbers of improper ascents, proper ascents, left-to-right minima and right-to-left minina. In the final part, we first give a symmetric decomposition of the joint distribution of the ascent-plateau and left ascent-plateau statistics, and then we show that the $q$-ascent-plateau polynomials are bi-$γ$-positive, where $q$ marks the number of left-to-right minima. - 6 March 2025
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 550 (1)
Analytical properties of derivative polynomials
- 6 March 2025
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 550 (1)
Analytical properties of derivative polynomials
- Open Access
Determinantal representations of alternating run polynomials
Based on a determinantal formula for the higher derivative of a quotient of two functions, we first present the determinantal expressions of Eulerian polynomials and Andre polynomials. In particular, we discover that the Euler number (number of alternating permutations) can be expressed as a lower Hessenberg determinant. We then investigate the determinantal representations of the up-down run polynomials and the types A and B alternating run polynomials. As applications, we deduce several new recurrence relations, which imply the multiplicity of -1 in these three kinds of polynomials. And then, we provide two determinantal representations for the alternating run polynomials of dual Stirling permutations. In particular, we discover a close connection between the alternating run polynomials of dual Stirling permutations and the type B Eulerian polynomials.
Open AccessDeterminantal representations of alternating run polynomials
Based on a determinantal formula for the higher derivative of a quotient of two functions, we first present the determinantal expressions of Eulerian polynomials and Andre polynomials. In particular, we discover that the Euler number (number of alternating permutations) can be expressed as a lower Hessenberg determinant. We then investigate the determinantal representations of the up-down run polynomials and the types A and B alternating run polynomials. As applications, we deduce several new recurrence relations, which imply the multiplicity of -1 in these three kinds of polynomials. And then, we provide two determinantal representations for the alternating run polynomials of dual Stirling permutations. In particular, we discover a close connection between the alternating run polynomials of dual Stirling permutations and the type B Eulerian polynomials.
- Open Access
Normal ordered grammars
We introduce the theory of normal ordered grammars, which gives a natural generalization of the normal ordering problem. To illustrate the main idea, we explore normal ordered grammars associated with the Eulerian polynomials and the second-order Eulerian polynomials. In particular, we present a normal ordered grammatical interpretation for the (cdes,cyc) (p,q)-Eulerian polynomials, where cdes and cyc are the cycle descent and cycle statistics, respectively. The exponential generating function for a family of polynomials, generated by a normal ordered grammar associated with the second-order Eulerian polynomials, reveals an interesting feature: its expression involves the generating function for Catalan numbers as its exponent. In the final part, we discuss some normal ordered grammars related to the type B Eulerian polynomials. A normal ordered grammatical interpretation of the up-down run polynomial is also established.
Open AccessNormal ordered grammars
We introduce the theory of normal ordered grammars, which gives a natural generalization of the normal ordering problem. To illustrate the main idea, we explore normal ordered grammars associated with the Eulerian polynomials and the second-order Eulerian polynomials. In particular, we present a normal ordered grammatical interpretation for the (cdes,cyc) (p,q)-Eulerian polynomials, where cdes and cyc are the cycle descent and cycle statistics, respectively. The exponential generating function for a family of polynomials, generated by a normal ordered grammar associated with the second-order Eulerian polynomials, reveals an interesting feature: its expression involves the generating function for Catalan numbers as its exponent. In the final part, we discuss some normal ordered grammars related to the type B Eulerian polynomials. A normal ordered grammatical interpretation of the up-down run polynomial is also established.
- Open Access
On the joint distributions of succession and Eulerian statistics
The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. As an generalization a result of Diaconis-Evans-Graham (Adv. in Appl. Math., 61 (2014), 102-124), we show that two triple set-valued statistics of permutations are equidistributed on symmetric groups. We then introduce the definition of proper left-to-right minimum, and discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc (p,q)-Eulerian polynomials and the joint distribution of succession and Eulerian-type statistics. In particular, we give a concise derivation of the generating function for a six-variable Eulerian polynomials.
Open AccessOn the joint distributions of succession and Eulerian statistics
The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. As an generalization a result of Diaconis-Evans-Graham (Adv. in Appl. Math., 61 (2014), 102-124), we show that two triple set-valued statistics of permutations are equidistributed on symmetric groups. We then introduce the definition of proper left-to-right minimum, and discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc (p,q)-Eulerian polynomials and the joint distribution of succession and Eulerian-type statistics. In particular, we give a concise derivation of the generating function for a six-variable Eulerian polynomials.
- Open Access
Differential operators, grammars and Young tableaux
In algebraic combinatorics and formal calculation, context-free grammar is defined by a formal derivative based on a set of substitution rules. In this paper, we investigate this issue from three related viewpoints. Firstly, we introduce a differential operator method. As one of the applications, we deduce a new grammar for the Narayana polynomials. Secondly, we investigate the normal ordered grammars associated with the Eulerian polynomials. Thirdly, motivated by the theory of differential posets, we introduce a box sorting algorithm which leads to a bijection between the terms in the expansion of $(cD)^nc$ and a kind of ordered weak set partitions, where $c$ is a smooth function in the indeterminate $x$ and $D$ is the derivative with respect to $x$. Using a map from ordered weak set partitions to standard Young tableaux, we find an expansion of $(cD)^nc$ in terms of standard Young tableaux. Combining this with the theory of context-free grammars, we provide a unified interpretations for the Ramanujan polynomials, André polynomials, left peak polynomials, interior peak polynomials, Eulerian polynomials of types $A$ and $B$, $1/2$-Eulerian polynomials, second-order Eulerian polynomials, and Narayana polynomials of types $A$ and $B$ in terms of standard Young tableaux. Along the same lines, we present an expansion of the powers of $c^kD$ in terms of standard Young tableaux, where $k$ is a positive integer. In particular, we provide four interpretations for the second-order Eulerian polynomials. All of the above apply to the theory of formal differential operator rings.Open AccessDifferential operators, grammars and Young tableaux
In algebraic combinatorics and formal calculation, context-free grammar is defined by a formal derivative based on a set of substitution rules. In this paper, we investigate this issue from three related viewpoints. Firstly, we introduce a differential operator method. As one of the applications, we deduce a new grammar for the Narayana polynomials. Secondly, we investigate the normal ordered grammars associated with the Eulerian polynomials. Thirdly, motivated by the theory of differential posets, we introduce a box sorting algorithm which leads to a bijection between the terms in the expansion of $(cD)^nc$ and a kind of ordered weak set partitions, where $c$ is a smooth function in the indeterminate $x$ and $D$ is the derivative with respect to $x$. Using a map from ordered weak set partitions to standard Young tableaux, we find an expansion of $(cD)^nc$ in terms of standard Young tableaux. Combining this with the theory of context-free grammars, we provide a unified interpretations for the Ramanujan polynomials, André polynomials, left peak polynomials, interior peak polynomials, Eulerian polynomials of types $A$ and $B$, $1/2$-Eulerian polynomials, second-order Eulerian polynomials, and Narayana polynomials of types $A$ and $B$ in terms of standard Young tableaux. Along the same lines, we present an expansion of the powers of $c^kD$ in terms of standard Young tableaux, where $k$ is a positive integer. In particular, we provide four interpretations for the second-order Eulerian polynomials. All of the above apply to the theory of formal differential operator rings. - 11 October 2023
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 342, 355-361
Commuting Eulerian operators
- 11 October 2023
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 342, 355-361
Commuting Eulerian operators
- 9 January 2023
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (5)
Several improved asymptotic normality criteria and their applications to graph polynomials
- 9 January 2023
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (5)
Several improved asymptotic normality criteria and their applications to graph polynomials
- Open Access
A symmetric decomposition of the Boros-Moll polynomials
In their study of a quartic integral, Boros and Moll introduced a special case of Jacobi polynomials, which are now known as the Boros-Moll polynomials. In this paper, we study a symmetric decomposition of Boros-Moll polynomials. We discover that both of the polynomials in the symmetric decomposition are alternatingly gamma-positive polynomials.
Open AccessA symmetric decomposition of the Boros-Moll polynomials
In their study of a quartic integral, Boros and Moll introduced a special case of Jacobi polynomials, which are now known as the Boros-Moll polynomials. In this paper, we study a symmetric decomposition of Boros-Moll polynomials. We discover that both of the polynomials in the symmetric decomposition are alternatingly gamma-positive polynomials.
- 26 May 2022
- Published by Elsevier in Discrete Mathematics
- Vol. 345 (10)
Generalized signed graphs of large girth and large chromatic number
- 26 May 2022
- Published by Elsevier in Discrete Mathematics
- Vol. 345 (10)
Generalized signed graphs of large girth and large chromatic number