相关论文: Transformation and symmetries for the Andrews-Garv…

A classic problem in enumerative combinatorics is to count the number of derangements, that is, permutations with no fixed point. Inspired by a recent generalization to facet derangements of the hypercube by Gordon and McMahon, we…

Cubic blocks are studied assembled from linear operators $\mathcal R$ acting in the tensor product of $d$ linear "spin" spaces. Such operator is associated with a linear transformation $A$ in a vector space over a field $F$ of a finite…

We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduce a rank-like function, establish inequalities with the…

Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…

George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third order mock theta functions $\omega(q)$ and $\nu(q)$, thereby extending their earlier results with the second author.…

Given a finite group $G$ acting on a set $X$ let $\delta_k(G,X)$ denote the proportion of elements in $G$ that have exactly $k$ fixed points in $X$. Let $\mathrm{S}_n$ denote the symmetric group acting on $[n]=\{1,2,\dots,n\}$. For…

Carlitz and Scoville in 1973 considered a four variable polynomial that enumerates permutations in $\mathfrak{S}_n$ with respect to the parity of its descents and ascents. In recent work, Pan and Zeng proved a $q$-analogue of…

It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences modulo…

The coefficients of the generating function $(q;q)^\alpha_\infty$ produce $p_\alpha(n)$ for $\alpha \in \mathbb{Q}$. In particular, when $\alpha = -1$, the partition function is obtained. Recently, Chan and Wang identified and proved…

We study the Iwasawa-type decomposition of an open subset of SL(n,C) as SU(p,q)AN. We show that the dressing action of SU(p,q) is globally defined on the space of admissible elements in AN. We also show that the space of admissible elements…

A combined analysis of both $e^+\,e^-$ (LEP, SLD) and $p\,p$ (RHIC-PHENIX and LHC-ALICE) hadroproduction processes are done for the first time for the vector meson nonet at the next-to-leading order (NLO) using a model with broken SU(3)…

A simple quark-diquark model for nucleon and $\Lambda$ structure is used to calculate leading twist light-cone fragmentation functions for a quark to inclusively decay into P or $\Lambda$. The parameters of the model are determined by…

New congruences are found for Andrews' smallest parts partition function spt(n). The generating function for spt(n) is related to the holomorphic part alpha(24z) of a certain weak Maass form M(z) of weight 3/2. We show that a normalized…

In important recent developments, new Sasaki-Einstein spaces $Y^{p,q}$ and conformal gauge theories dual to $AdS_5\times Y^{p,q}$ have been constructed. We consider a stack of N D3-branes and M wrapped D5-branes at the apex of a cone over…

We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar calculations in other cases. Moreover, we…

Bringmann, Mahlburg, and Rhoades have found asymptotic expressions for all moments of the partition statistics rank and crank. In this work we extend their methods to higher ranks. The $T$-rank, introduced by Garvan, for odd integers T=3 is…

An algebraic description of basic discrete symmetries (space inversion P, time reversal T, charge conjugation C and their combinations PT, CP, CT, CPT) is studied. Discrete subgroups {1,P,T,PT} of orthogonal groups of multidimensional…

We construct for $d\geq 2$ and $\epsilon>0$ a $d$-generated $p$-group $\Gamma$, which in an asymptotic sense behaves almost like a $d$-generated free pro-$p$-group. We show that a subgroup of index $p^n$ needs $(d-\epsilon)p^n$ generators,…

J.-P. Thouvenot and the author showed via different approaches that the centralizer of a mixing rank-one infinite measure preserving transformation was trivial. In this note the author presents his joining proof. We also consider…

We compute genus two partition functions in two dimensional conformal field theories at large central charge, focusing on surfaces that give the third Renyi entropy of two intervals. We compute this for generalized free theories and for…