Bruce E. Sagan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Bruce E. Sagan has a total of 125 co-authors. Here are the top co-authors by number of shared publications:
- Vincent Vatter
University of Florida
8 shared publications - Jinting Liang
Department of Mathematics Michigan State University 48824-1027 East Lansing MI USA
4 shared publications - Miklos Bona
Department of Mathematics University of Florida Gainesville FL 32611-8105
4 shared publications - Joshua P. Swanson
Department of Mathematics, University of Southern California, Los Angeles, USA
3 shared publications - Theodore Dokos
Department of Mathematics University of California
3 shared publications - Tim Dwyer
Department of Mathematics Dartmouth College
3 shared publications
Latest Publications
- 2 May 2026
- Published by Springer Nature in Order
- Vol. 43 (2) , 21
Log-Concavity and Log-Convexity via Distributive Lattices
- 2 May 2026
- Published by Springer Nature in Order
- Vol. 43 (2) , 21
Log-Concavity and Log-Convexity via Distributive Lattices
- Open Access
- 26 February 2026
- Published by Cambridge University Press (CUP) in Forum of Mathematics, Sigma
- Vol. 14, e30
Hyperbinary partitions and q -deformed rationals
A hyperbinary partition of the nonnegative integer n is a partition where every part is a power of $2$ and every power of $2$ appears at most twice. We give three applications of the length generating function for such partitions, denoted by $h_q(n)$ . Morier-Genoud and Ovsienko defined the q -analogue of a rational number $[r/s]_q$ in various ways, most of which depend directly or indirectly on the continued fraction expansion of $r/s$ . As our first application we show that $[r/s]_q=q\,h_q(n-1)/h_q(n)$ where $r/s$ occurs as the n th entry in the Calkin-Wilf enumeration of the non-negative rationals. Next we consider fence posets which are those which can be obtained from a sequence of chains by alternately pasting together maxima and minima. For every n we show there is a fence poset ${\cal F}(n)$ whose lattice of order ideals is isomorphic to the poset of hyperbinary partitions of n ordered by refinement. For our last application, Morier-Genoud and Ovsienko also showed that $[r/s]_q$ can be computed by taking products of certain matrices which are q -analogues of the standard generators for the special linear group $\operatorname {\mathrm {SL}}(2,{\mathbb Z})$ . We express the entries of these products in terms of the polynomials $h_q(n)$ .- 26 February 2026
- Published by Cambridge University Press (CUP) in Forum of Mathematics, Sigma
- Vol. 14, e30
Open AccessHyperbinary partitions and q -deformed rationals
A hyperbinary partition of the nonnegative integer n is a partition where every part is a power of $2$ and every power of $2$ appears at most twice. We give three applications of the length generating function for such partitions, denoted by $h_q(n)$ . Morier-Genoud and Ovsienko defined the q -analogue of a rational number $[r/s]_q$ in various ways, most of which depend directly or indirectly on the continued fraction expansion of $r/s$ . As our first application we show that $[r/s]_q=q\,h_q(n-1)/h_q(n)$ where $r/s$ occurs as the n th entry in the Calkin-Wilf enumeration of the non-negative rationals. Next we consider fence posets which are those which can be obtained from a sequence of chains by alternately pasting together maxima and minima. For every n we show there is a fence poset ${\cal F}(n)$ whose lattice of order ideals is isomorphic to the poset of hyperbinary partitions of n ordered by refinement. For our last application, Morier-Genoud and Ovsienko also showed that $[r/s]_q$ can be computed by taking products of certain matrices which are q -analogues of the standard generators for the special linear group $\operatorname {\mathrm {SL}}(2,{\mathbb Z})$ . We express the entries of these products in terms of the polynomials $h_q(n)$ . - 8 August 2025
- Published by Elsevier in Discrete Mathematics
- Vol. 349 (1)
Modified difference ascent sequences and Fishburn structures
- 8 August 2025
- Published by Elsevier in Discrete Mathematics
- Vol. 349 (1)
Modified difference ascent sequences and Fishburn structures
- 7 August 2025
- Published by Elsevier in Discrete Mathematics
- Vol. 349 (2)
Generalized Euler numbers and ordered set partitions
- 7 August 2025
- Published by Elsevier in Discrete Mathematics
- Vol. 349 (2)
Generalized Euler numbers and ordered set partitions
- 24 March 2025
- Published by Springer Nature in Annals of Combinatorics
- Vol. 30 (2) , 365-395
Stirling Numbers for Complex Reflection Groups
- 24 March 2025
- Published by Springer Nature in Annals of Combinatorics
- Vol. 30 (2) , 365-395
Stirling Numbers for Complex Reflection Groups
- 16 November 2024
- Published by Springer Nature in Annals of Combinatorics
- Vol. 30 (1) , 155-176
Elementary Symmetric Partitions
- 16 November 2024
- Published by Springer Nature in Annals of Combinatorics
- Vol. 30 (1) , 155-176
Elementary Symmetric Partitions
- Open Access
Stirling numbers for complex reflection groups
In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G. The Stirling numbers of the first and second kind are defined via the Whitney numbers of the first and second kind, respectively, of the intersection lattice of G. For the groups G(m,p,n), these numbers and polynomials can be given combinatorial interpretations in terms of various statistics. The ordered version of ths q-Stirling numbers of the second kind also show up in conjectured Hilbert series for certain super coinvariant algebras.
Open AccessStirling numbers for complex reflection groups
In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G. The Stirling numbers of the first and second kind are defined via the Whitney numbers of the first and second kind, respectively, of the intersection lattice of G. For the groups G(m,p,n), these numbers and polynomials can be given combinatorial interpretations in terms of various statistics. The ordered version of ths q-Stirling numbers of the second kind also show up in conjectured Hilbert series for certain super coinvariant algebras.
- Open Access
Log-concavity and log-convexity via distributive lattices
We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal Lemma to prove log-concavity and log-convexity of various sequences involving lattice paths (Catalan, Motzkin and large Schröder numbers), intervals in Young's lattice, order polynomials, specializations of Schur and Schur Q-functions, Lucas sequences, descent and peak polynomials of permutations, pattern avoidance, set partitions, and noncrossing partitions. We end with a section with conjectures and outlining future directions.
Open AccessLog-concavity and log-convexity via distributive lattices
We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal Lemma to prove log-concavity and log-convexity of various sequences involving lattice paths (Catalan, Motzkin and large Schröder numbers), intervals in Young's lattice, order polynomials, specializations of Schur and Schur Q-functions, Lucas sequences, descent and peak polynomials of permutations, pattern avoidance, set partitions, and noncrossing partitions. We end with a section with conjectures and outlining future directions.
- Open Access
Chromatic symmetric functions and change of basis
We prove necessary conditions for certain elementary symmetric functions, $e_λ$, to appear with nonzero coefficient in Stanley's chromatic symmetric function as well as in the generalization considered by Shareshian and Wachs. We do this by first considering the expansion in the monomial or Schur basis and then performing a basis change. Using the former, we make a connection with two fundamental graph theory invariants, the independence and clique numbers. This allows us to prove nonnegativity of three-column coefficients for all natural unit interval graphs. The Schur basis permits us to give a new interpretation of the coefficient of $e_n$ in terms of tableaux. We are also able to give an explicit formula for that coefficient.Open AccessChromatic symmetric functions and change of basis
We prove necessary conditions for certain elementary symmetric functions, $e_λ$, to appear with nonzero coefficient in Stanley's chromatic symmetric function as well as in the generalization considered by Shareshian and Wachs. We do this by first considering the expansion in the monomial or Schur basis and then performing a basis change. Using the former, we make a connection with two fundamental graph theory invariants, the independence and clique numbers. This allows us to prove nonnegativity of three-column coefficients for all natural unit interval graphs. The Schur basis permits us to give a new interpretation of the coefficient of $e_n$ in terms of tableaux. We are also able to give an explicit formula for that coefficient.