13 papers
Matchings and shape-Wilf-Equivalence of sets of patterns of length three II: Quadruples and Quintuples
Sucharita Biswas, Umesh Shankar, Sivaramakrishnan Sivasubramanian
Building on our classification of shape-Wilf-equivalence classes for triples of patterns of length three, we complete the classification for quadruples and quintuples. The larger p…
Multivariate stability of powered triangular recurrences and parametrised Eulerian polynomials
Umesh Shankar
We prove multivariate stability for a class of affine triangular recurrences whose two coefficients are raised to an arbitrary positive integer power. The variables keep track of c…
Matchings and shape-Wilf-Equivalence of sets of patterns of length three I: Triples
Sucharita Biswas, Umesh Shankar, Sivaramakrishnan Sivasubramanian
Permutation pattern avoidance on Ferrers boards has become a central topic in enumerative combinatorics with important connections to matchings, set partitions, and other combinato…
Avoiding patterns with three distinct letters in Canon permutations
Umesh Shankar
We study avoidance of patterns of length with three distinct letters in canon permutations. We reduce the problem to studying pattern avoidance in lattice words and show that t…
Caged subsequences in permutations
Niranjan Balachandran, Omkar Ramdas, Umesh Shankar
Given a sequence of reals, a subsequence is said to be "caged" if the largest and smallest among the member…
Oddtown and eventown theorems for lattice paths
Umesh Shankar
For North-East lattice paths (which we simply call lattice paths), we define intersection in terms of common edges. We prove that a family of paths from to in which…
Homogenized Graphical Shi Arrangements and Deformed Dumont Permutations
Sauvik Poddar, Rutuja Sawant, Umesh Shankar
We introduce the homogenized graphical Shi arrangement associated with a simple undirected graph , which serves as a broad generalization of classical deformations of the braid…
Ordinal and disjoint sums of partially ordered patterns
Sucharita Biswas, Umesh Shankar, Sivaramakrishnan Sivasubramanian
Partially ordered patterns (POPs) generalize the classical notion of permutation patterns within the framework of pattern avoidance. Building on recent work by Burstein, Han, Kitae…
Log-concavity of rows of triangular arrays satisfying a certain super-recurrence
Umesh Shankar
Recurrences of the form \begin{equation*} T(n,k) = (αn+βk +γ) \ T(n-1,k) + (α'n+β'k+γ')\ T(n-1,k-1)+δ_{n,0}δ_{k,0}. \end{equation*} show up as the recurrence for many well-studied…
A descent-excedance correspondence in colored permutation groups
Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian
It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed…
Two bijections in the spirit of the transformation fondamentale
Umesh Shankar
In this short paper, we give bijective proofs of two recent equidistribution results connecting cyclic and linear statistics in the spirit of the Foata's ``transformation fondament…
Synchronicity of descent and excedance enumerators in the alternating subgroup
Umesh Shankar
Generalising the work of Dey, we define the notion of ultra-synchronicity of sequences of real numbers. Let be the number of even permutations wit…
Canonical reduced words and signed descent length enumeration in Coxeter groups
Umesh Shankar, Sivaramakrishnan Sivasubramanian
Reifegerste and independently, Petersen and Tenner studied a statistic on permutations in . Two other studied statistics on are…