10 citations · 21 across the 23 of their papers we have counts for
29 papers
Andrews--Gordon type identities with parity restrictions through particle motion
Jehanne Dousse, Jihyeug Jang
In this paper, we use the particle motion bijection introduced by Warnaar and developed by the two authors, Jouhet and Konan, to study q-series and partition identities of the Andr…
Bailey pairs and quantum -series identites. I. The classical identities
Jehanne Dousse, Jeremy Lovejoy
We use Bailey pairs to prove -series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the s…
Andrews--Gordon and Stanton type identities: bijective and Bailey lemma approaches
Jehanne Dousse, Jihyeug Jang, Frédéric Jouhet
In 2018, Stanton proved two types of generalisations of the celebrated Andrews--Gordon and Bressoud identities (in their -series version): one with a similar shape to the origin…
Combinatorial approach to Andrews-Gordon and Bressoud type identities
Jehanne Dousse, Frédéric Jouhet, Isaac Konan
We provide combinatorial tools inspired by work of Warnaar to give combinatorial interpretations of the sum sides of the Andrews-Gordon and Bressoud identities. More precisely, we…
Bilateral Bailey Lattices and Andrews-Gordon Type Identities
Jehanne Dousse, Frédéric Jouhet, Isaac Konan
We show that the Bailey lattice can be extended to a bilateral version in just a few lines from the bilateral Bailey lemma, using a very simple lemma transforming bilateral Bailey…
Characters of level standard modules of as generating functions for generalised partitions
Jehanne Dousse, Isaac Konan
We give a new simple formula for the energy function of a level perfect crystal of type introduced by Kang, Kashiwara and Misra. We use this to give several express…
A -multisum identity arising from finite chain ring probabilities
Jehanne Dousse, Robert Osburn
In this note, we prove a general identity between a -multisum and a sum of products of quotients of theta functions. The -multisum recently arose in t…
Partition identities from higher level crystals of
Jehanne Dousse, Leonard Hardiman, Isaac Konan
We study perfect crystals for the standard modules of the affine Lie algebra at all levels using the theory of multi-grounded partitions. We prove a family of partition…
New companions to the Andrews--Gordon identities motivated by commutative algebra
Pooneh Afsharijoo, Jehanne Dousse, Frédéric Jouhet +1
We give a proof of a recent combinatorial conjecture due to the first author, which was discovered in the framework of commutative algebra. This result gives rise to new companions…
Multi-grounded partitions and character formulas
Jehanne Dousse, Isaac Konan
We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express chara…
Cylindric partitions and some new Rogers-Ramanujan identities
Sylvie Corteel, Jehanne Dousse, Ali K. Uncu
We study the generating functions for cylindric partitions with profile for all such that . This allows us to discover and prove seven…
Generalisations of Capparelli's and Primc's identities, I: coloured Frobenius partitions and combinatorial proofs
Jehanne Dousse, Isaac Konan
In these two companion papers, we give infinite families of partition identities which generalise Primc's and Capparelli's identities, and study their consequences on the theory of…
Generalisations of Capparelli's and Primc's identities, II: perfect crystals and explicit character formulas
Jehanne Dousse, Isaac Konan
In the first paper of this series, we gave infinite families of coloured partition identities which generalise Primc's and Capparelli's classical identities. In this second paper,…
On partition identities of Capparelli and Primc
Jehanne Dousse
We show that, up to multiplication by a factor , the weighted words version of Capparelli's identity is a particular case of the weighted words version o…
Asymptotics for skew standard Young tableaux via bounds for characters
Jehanne Dousse, Valentin Féray
We are interested in the asymptotics of the number of standard Young tableaux of a given skew shape . We mainly restrict ourselves to the case where both diagrams ar…
Generalizations of Capparelli's identity
Jehanne Dousse, Jeremy Lovejoy
Using jagged overpartitions, we give three generalizations of a weighted word version of Capparelli's identity due to Andrews, Alladi, and Gordon and present several corollaries.
The method of weighted words revisited
Jehanne Dousse
Alladi and Gordon introduced the method of weighted words in 1993 to prove a refinement and generalisation of Schur's partition identity. Together with Andrews, they later used it…
An overpartition analogue of -binomial coefficients, II: combinatorial proofs and -log concavity
Jehanne Dousse, Byungchan Kim
In a previous paper, we studied an overpartition analogue of Gaussian polynomials as the generating function for overpartitions fitting inside an rectangle. Here, we a…
On a Rogers-Ramanujan type identity from crystal base theory
Jehanne Dousse, Jeremy Lovejoy
We refine and generalise a Rogers-Ramanujan type partition identity arising from crystal base theory. Our proof uses the variant of the method of weighted words recently introduced…
Weighted dependency graphs and the Ising model
Jehanne Dousse, Valentin Féray
Weighted dependency graphs have been recently introduced by the second author, as a toolbox to prove central limit theorems. In this paper, we prove that spins in the -dimension…
Unification, refinements and companions of generalisations of Schur's theorem
Jehanne Dousse
We prove a general theorem on overpartitions with difference conditions that unifies generalisations of Schur's theorem due to Alladi-Gordon, Andrews, Corteel-Lovejoy and the autho…
Siladić's theorem: weighted words, refinement and companion
Jehanne Dousse
In a previous paper, the author gave a combinatorial proof and refinement of Siladić's theorem, a Rogers-Ramanujan type partition identity arising from the study of Lie algebras. H…
A generalisation of a second partition theorem of Andrews to overpartitions
Jehanne Dousse
In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur's celebrated partition identity (1926). Andrews' two generalisations of…
An overpartition analogue of the -binomial coefficients
Jehanne Dousse, Byungchan Kim
We define an overpartition analogue of Gaussian polynomials (also known as -binomial coefficients) as a generating function for the number of overpartitions fitting inside the $…