Adding an implementation of the Abreu-Nigro sym funcs.

Author: tscrim

src/doc/en/reference/combinat/module_list.rst

@@ -309,6 +309,7 @@ Comprehensive Module List
     sage/combinat/set_partition
     sage/combinat/set_partition_iterator
     sage/combinat/set_partition_ordered
+    sage/combinat/sf/abreu_nigro
     sage/combinat/sf/all
     sage/combinat/sf/character
     sage/combinat/sf/classical

src/doc/en/reference/references/index.rst

@@ -265,6 +265,18 @@ REFERENCES:
               Symposium, Volume 51, page 20.
               Australian Computer Society, Inc. 2006.
 
+.. [AN2021] Alex Abreu and Antonio Nigro. *Chromatic symmetric functions from
+            the modular law*. J. Combin. Theory Ser. A, **180** (2021), paper
+            no. 105407. :arxiv:`2006.00657`.
+
+.. [AN2021II] Alex Abreu and Antonio Nigro. *A symmetric function of increasing
+              forests*. Forum Math. Sigma, **9** No. 21 (2021), Id/No e35.
+              :arxiv:`2006.08418`.
+
+.. [AN2023] Alex Abreu and Antonio Nigro. *Splitting the cohomology of Hessenberg
+            varieties and e-positivity of chromatic symmetric functions*. 
+            Preprint (2023). :arxiv:`2304.10644`.
+
 .. [Ang1997] B. Anglès. 1997. *On some characteristic polynomials attached to
              finite Drinfeld modules.* manuscripta mathematica 93, 1 (01 Aug 1997),
              369–379. https://doi.org/10.1007/BF02677478

src/sage/combinat/posets/poset_examples.py

@@ -500,6 +500,40 @@ def DivisorLattice(n, facade=None):
         return FiniteLatticePoset(hasse, elements=Div_n, facade=facade,
                                   category=FiniteLatticePosets())
 
+    @staticmethod
+    def HessenbergPoset(H):
+        r"""
+        Return the poset associated to a Hessenberg function ``H``.
+
+        A *Hessenberg function* (of length `n`) is a function `H: \{1,\ldots,n\}
+        \to \{1,\ldots,n\}` such that `\max(i, H(i-1)) \leq H(i) \leq n` for all
+        `i` (where `H(0) = 0` by convention). The corresponding poset is given
+        by `i < j` if and only if `H(i) < j`. These correspond to the natural
+        unit interval order posets.
+
+        INPUT:
+
+        - ``H`` -- list; the Hessenberg function values
+
+        EXAMPLES::
+
+            sage: P = posets.HessenbergPoset([2, 3, 5, 5, 5]); P
+            Finite poset containing 5 elements
+            sage: P.cover_relations()
+            [[2, 4], [2, 5], [1, 3], [1, 4], [1, 5]]
+
+        TESTS::
+
+            sage: P = posets.HessenbergPoset([2, 2, 6, 4, 5, 6])
+            Traceback (most recent call last):
+            ...
+            ValueError: [2, 2, 6, 4, 5, 6] is not a Hessenberg function
+        """
+        n = len(H)
+        if not all(max(i+1, H[i-1]) <= H[i] for i in range(1, n)) or H[-1] > n:
+            raise ValueError(f"{H} is not a Hessenberg function")
+        return Poset((tuple(range(1, n+1)), lambda i, j: H[i-1] < j))
+
     @staticmethod
     def IntegerCompositions(n):
         """